System and a method for mapping a magnetic field

ABSTRACT

A system for mapping a magnetic-field in a volume-of-interest comprising a magnetic-field transmitter, generating a magnetic-field in the volume-of-interest, a freestanding magnetic-field detector operative to freely move within the volume-of-interest, a pose-information-acquisition-module and a processor. The detector acquires measurements of flux of the magnetic-field at a plurality of poses. The pose-information-acquisition-module measures information related to the pose of the detector. The processor determines pose-related-information respective of at least a portion of the measurements according to the information related to the pose of the detector. The processor estimates the entire set of parameters of a magnetic-field model template according to the magnetic-field flux measurement and the respective poses-related-information thereof. The processor incorporates the entire set of parameters into the magnetic-field model template, thereby determining the magnetic-field model. The entire set of parameters includes the coefficients, the order the number and location of the centers of expansion of the magnetic-field model.

FIELD OF THE DISCLOSED TECHNIQUE

The disclosed technique relates to magnetic fields, in general, and tosystems and methods for mapping magnetic fields, in particular.

BACKGROUND OF THE DISCLOSED TECHNIQUE

Applications of tracking an object, within a volume of interest, areknown in the art. For example, tracking a helmet, worn by a pilot in acockpit is used to determine the location and orientation that the pilotis looking at (i.e., by further determining the gaze direction of theeye of the pilot). Tracking a catheter, within a body of a patient, maybe used to display a representation of the catheter on an image of thebody (e.g., an X-Ray image, CT image, MRI image, PET image and thelike). Tracking various body parts of a person may be used to emulatethe movement of that person in a virtual reality environment.

Systems for tracking an object, within a volume of interest usingmagnetic fields, are known in the art. These systems are referred toherein as “magnetic tracking systems”. Magnetic tracking systems trackthe object by repeatedly determining the location and orientation of theobject, in the volume of interest, relative to a coordinate systemassociated with the magnetic tracking system. The term “pose” refershereinafter to either location, orientation or both. The term “location”relates to the coordinates of an object (i.e., according to a determinedcoordinate system such as X, Y, Z) and the term “orientation” relates tothe direction of the object in the determined coordinate system (e.g.,Eulers angles). The term “magnetic coordinate system” refers hereinafterto a coordinate system associated with the magnetic tracking system. Ingeneral, magnetic tracking systems employ a magnetic field transmitterand a magnetic field detector. The magnetic field transmitter may employseveral magnetic field generators (e.g., coils with electric currentflowing there through). The magnetic field detector may employ severalmagnetic field sensors (e.g., coils with electric current inducedtherein, hall-effect sensors). In general, for the purpose of magnetictracking, the number of generators times the number of sensors should atleast equal the number of required location and orientation parameters(e.g., the number of required location and orientation parameters may besix, three for location and three for orientation). According oneconfiguration of magnetic tracking systems, the magnetic fieldtransmitter is fixed at a known pose in the volume of interest and themagnetic field detector is mounted on the tracked object. According toanother configuration of magnetic tracking systems, the magnetic fieldtransmitter is mounted on the tracked object and the magnetic fielddetector is fixed at a known pose in the volume of interest.

To determine the position of the tracked object, within a volume ofinterest, using magnetic fields, the amplitude and direction of themagnetic field at each location in the volume of interest should beknown (i.e., either measured or computed). The amplitude and directionof the magnetic field is referred to hereinafter as the “magnetic fieldvector”. The ensemble of magnetic field vectors at correspondinglocations in the volume of interest is referred to hereinafter as the“magnetic field map”. The magnetic tracking system determines the poseof a tracked object by measuring the magnetic flux at that pose. Themagnetic tracking system determines the magnetic field vector accordingto the measured magnetic flux, and determines the pose corresponding tothat magnetic field vector according to the magnetic field map.

A magnetic field map may have one of several forms. Accordingly, themagnetic field map may have the form of a physical model relating eachlocation in the volume of interest with an amplitude and direction ofthe magnetic field. The physical model includes physical parameters. Forexample, when the magnetic field is generated by a coil, the magneticfield model may be that of a dipole with physical parameters such ascoil radius and the number of turns of the coil. Alternatively, themagnetic field map may have the form of a mathematical model, withoutany knowledge of the physical parameters of the magnetic field (e.g.,polynomial, spline). According to yet another alternative, the magneticfield map may be in the form of a Look Up Table (LUT) associatingbetween a selected number of known locations in the volume of interestwith corresponding values of the magnetic field vectors at theseselected locations. The value of the magnetic field vectors, betweenentries in the LUT, is determined according to an interpolation scheme(e.g., an interpolation function such as a straight line, a sincfunction etc).

The magnetic field map may be determined at the manufacturing stage ofthe magnetic field transmitter. However, such a map does not allow forall the interferences introduced to the magnetic field in a specificvolume of interest (e.g., interferences caused by ferromagnetic objectsor other electromagnetic transmitters within the volume of interest).The magnetic field map may be determined, prior to tracking,individually for each volume of interest. This map includes theinterferences (i.e., when those exist) introduced to the magnetic fieldin the volume of interest (e.g., due to metallic objects present in thevolume of interest). Accordingly, the magnetic field transmitter isactivated and the magnetic field detector is moved through a pluralityof known poses in the volume of interest. The magnetic field detectormeasures the magnetic field vector at each known location. A processorprocesses these measurements and produces the magnetic field map. Whenthe magnetic field map is a physical model or a mathematical model, theprocessor estimates the parameters (i.e., the physical parameters or themathematical parameters) to determined the model that best fits themeasurements. When the magnetic field map is a LUT, the processorconstructs the LUT according to the measurements and the knownlocations. It is noted that the term “mapping” refers to herein after todetermining the magnetic field map. The terms “magnetic field model” and“model” will be used herein interchangeably.

Additionally, when the magnetic tracking system is required to determinethe pose of the tracked object in a coordinates system associated withthe volume of interest, the magnetic tracking system registers themagnetic field map with the coordinate system associated with the volumeof interest. The coordinate system associated with the volume ofinterest is referred to herein as the “reference coordinate system”. Theterm “registering” refers to determining a correspondence between theposes relative to the magnetic coordinate system and the poses relativeto the reference coordinate system. This reference coordinate system is,for example, the coordinate system of the airplane, the coordinatesystem of a virtual environment or the coordinate system of a medicalimage. Thus, the location and orientation of the tracked object is knownrelative to the reference coordinate system. The magnetic trackingsystem registers the magnetic field map with a reference coordinatesystem for example, by placing the magnetic field detector at a knownpose relative to the reference coordinate system and determines the poseof the magnetic field detector relative to the magnetic coordinatesystem. Alternatively, when the pose of the magnetic field transmitter,relative to the reference coordinate system, is known, each poserelative to the magnetic coordinate system is associated with arespective pose relative to the reference coordinate system.

The publication to Livingston et al., entitled “Magnetic TrackerCalibration for Improved Augmented Reality Registration”, directs to asystem and a method for mapping a magnetic field using LUT and forregistering the magnetic field map with a reference coordinate system.According to Livingston et al., a magnetic tracking system tracks thepose of a receiver attached to the object being tracked. However, metaland electromagnetic devices (e.g., computers, Cathode Ray Tubes, metalobjects and electrical wirings) distort the field created by thetransmitter. Therefore, the magnetic field model, used by the magnetictracking system, may be inaccurate. Thus, the system to Livingston et almaps the magnetic field and determines correction factors for eachlocation in the volume of interest. Accordingly, the receiver isattached to six degrees of freedom mechanical arm tracker, whichdetermines a vector of locations and orientations of the tip of the armrelative to the base of the arm. The coordinates system associated withthe mechanical tracking systems serves as the reference coordinatesystem. Thus, each pose determined by the magnetic tracking system, hasa pose determined by the mechanical tracking system associatedtherewith. The differences between these associated poses are used todetermine the corrections needed for the poses determined by themagnetic tracking system.

U.S. Pat. No. 5,847,976 to Lescourret, entitled “Method to Determine thePosition and Orientation of a Mobile System, Especially the Line OfSight in a Helmet Visor”, directs to analytic modeling ofelectromagnetic fields. These fields include a first electromagneticfield created by a transmitter, a second field created by eddy currentsinduced in metal object within the volume of interest by a first fieldand a third field created by currents induced in the tracked object(e.g., a helmet of a pilot) by the first and second fields. Each one ofthe three fields is characterized independently of the other fields bythe coefficients of a model associated with each field.

The first field is determined by measuring the field created by thetransmitter in free space. The field is measured at points ofmeasurements by translating a mechanical system bearing the sensorthrough these points. The parameters of a model of this field areestimated.

The second field is determined by measuring the field within the volumeof interest including the metal objects. The field is measured at pointsof measurements by translating a mechanical system bearing the sensorthrough these points. The parameters of a combined model including boththe first and the second field are estimated. The model of the firstfield is subtracted from this combined model.

The third field is determined by first plunging disturbance sources intothe magnetic field produced by the transmitter. The model of thedisturbance due to each disturbance source, at the sensor, is modeled asan explicit function of the existing mean field at the point of originof a coordinate system defining this source. Thus, the model of eachsource depends explicitly on the field into which each source is plungedinto. In a second stage, the sensor is plunged into the magnetic fieldand the disturbance caused by each source is determined by its model andof the mean magnetic field. In a third stage, disturbances due to thesources are summed. Finally, in a fourth stage, this sum is deductedfrom the measurement made by the sensor. In this way, all the parametersof the source model representing the phenomenon of disturbance producedby this source are independent of the field into which the sensor andall the sources are plunged.

The publication entitled “A Framework for of Electromagnetic SurgicalNavigation Systems” to Wu et al directs to employing a 3D opticalnavigation system to calibrate the measurement distortion of a magnetictracking system. To that end the publication to Wu et al directs toemploying a Lego robot which moves semi-statically within the desiredcalibration space with infrared tracking markers and the magnetictracking sensors attached thereto. The calibration process includesthree steps, registration between the magnetic tracking coordinatesystem and the optical tracking coordinate system and constructing anerror field of the magnetic tracking system and error correction andvalidation. The coordinate system of the optical tracking system isemployed as the “ground truth”. The error in Position error andorientation error can be expressed as 3D vectors. The publication to Wuet directs to two method to express the 3D error vectors in space. Oneis the KD trees and the other is fitting Bernstein polynomials.According to the publication to Wu et al, the magnetic field distortioncan be characterized by a Bernstein polynomial of the fourth order.

SUMMARY OF THE PRESENT DISCLOSED TECHNIQUE

It is an object of the disclosed technique to provide a novel system andmethod for mapping a magnetic field by freely moving a magnetic fielddetector within a volume of interest.

In accordance with the disclosed technique, there is thus provided asystem for mapping a magnetic field in a volume of interest. The systemincludes a magnetic field transmitter, at least one freestandingmagnetic field detector, at least one pose information acquisitionmodule and a processor. The processor is coupled with the magnetic fielddetector and with the at least one pose information acquisition module.The magnetic field transmitter generates a magnetic field in the volumeof interest. The at least one freestanding magnetic field detector, isoperative to freely move within the volume of interest and to acquire.The at least one freestanding magnetic field detector acquiresmeasurements of the flux of the magnetic field at a plurality of poses.The at least one pose information acquisition module measuresinformation related to the pose of the freestanding magnetic fielddetector. The processor determines pose related information respectiveof at least a portion of the measurements of the flux of the magneticfield according to the information related to the pose of thefreestanding magnetic field detector, measured by the at least one poseinformation acquisition module. The processor estimates the entire setof parameters of a magnetic field model template according to themagnetic field flux measurement and the respective pose relatedinformation thereof. The processor incorporates the entire set ofparameters into the magnetic field model template, thereby determiningthe magnetic field model. The entire set of parameters includes thecoefficients of the magnetic field model, the order of the magneticfield model, the number of the centers of expansion and the locations ofthe centers of expansion of the magnetic field model.

In accordance with the disclosed technique, there is thus provided amethod for mapping a magnetic field in a volume of interest. The methodincludes the procedures of freely moving a magnetic field detectorwithin the determined volume of interest, acquiring measurements of themagnetic field flux at a plurality of poses of the freestanding magneticfield detector within the volume of interest and determining poserelated information respective of at least a portion of the measurementof magnetic field flux. The method further includes the procedure ofestimating the entire set of parameters characterizing the magneticfield model according to the magnetic field flux measurements and therespective positions and orientations thereof. The entire set ofparameters includes the coefficients of the magnetic field model, theorder of the magnetic field model, the number of the centers ofexpansion and the locations of the centers of expansion of the magneticfield model.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed technique will be understood and appreciated more fullyfrom the following detailed description taken in conjunction with thedrawings in which:

FIG. 1 is a schematic illustration of a system for mapping a magneticfield in a volume of interest, constructed and operative in accordancewith an embodiment of the disclosed technique;

FIG. 2 is a schematic illustration of a system for mapping a magneticfield in a volume of interest, constructed and operative in accordancewith another embodiment of the disclosed technique;

FIG. 3 is a schematic illustration of a system, constructed andoperative in accordance with a further embodiment of the disclosedtechnique;

FIG. 4 is a schematic illustration of a system for mapping a magneticfield in a volume of interest, constructed and operative in accordancewith another embodiment of the disclosed technique;

FIG. 5A is a schematic illustration of a mapping handle and a magneticfield detector constructed and operative in accordance with a furtherembodiment of the disclosed technique;

FIG. 5B is a schematic illustration of a mapping handle and a magneticfield detector constructed and operative in accordance with anotherembodiment of the disclosed technique;

FIG. 5C is a schematic illustration of a mapping handle and a magneticfield detector constructed and operative in accordance with a furtherembodiment of the disclosed technique;

FIG. 5D is a schematic illustration of a mapping handle and a magneticfield detector constructed and operative in accordance with anotherembodiment of the disclosed technique;

FIG. 5E is a schematic illustration of a mapping handle and a magneticfield detector constructed and operative in accordance with a furtherembodiment of the disclosed technique;

FIG. 6 is a schematic illustration of a method for mapping a magneticfield in accordance with another embodiment of the disclosed technique;

FIG. 7 is a schematic illustration of an exemplary method for estimatingthe parameters of a magnetic field, in accordance with a furtherembodiment of the disclosed technique;

FIG. 8 is a schematic illustration of a system for mapping a magneticfield in a volume of interest, constructed and operative in accordancewith another embodiment of the disclosed technique;

FIG. 9 is a schematic illustration of a system for mapping a magneticfield in a volume of interest, constructed and operative in accordancewith a further embodiment of the disclosed technique; and

FIGS. 10A and 10B are schematic illustrations of a method for estimatingan entire set of parameter of a magnetic field model in accordance witha further embodiment of the disclosed technique.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The disclosed technique overcomes the disadvantages of the prior art byproviding a method and a system for mapping a magnetic field and thusdetermining the parameters characterizing a magnetic field model byfreely moving a magnetic field detector within the volume of interest.According to the disclosed technique a magnetic field detector ismounted on a freestanding mapping handle. Thus, the magnetic fielddetector is also freestanding. A magnetic field transmitter is activatedand produces a magnetic field in the volume of interest. An operatormoves the mapping handle in the volume of interest. The detectormeasures the magnetic field during the movement of the mapping handle. Aprocessor estimates the parameters characterizing the magnetic fieldmodel according to the measurements of the magnetic field.

According to one embodiment of the disclosed technique, the operatorfreely moves the mapping handle, and thus the magnetic field detector,randomly through the volume of interest. According to another embodimentof the disclosed technique, the operator is guided to freely move themapping handle to a plurality of mapping regions within the volume(e.g., audio instructions or visual instructions such as a displayshowing the volume of interest with representations of the regionsmarked on the display). The term “freely moves” refers to herein tounconstraint movement of the mapping handle (i.e., the trajectory ofmapping handle, from one pose in the volume of interest to another posein the volume of interest, has no constraints thereupon). Alternatively,the magnetic field detector may be mounted on a mechanical support suchas a mechanical arm capable of freely moving the magnetic field detectorthrough a plurality of poses (i.e., locations or orientation or both)within the volume of interest.

The poses of the detector, relative to the reference coordinate system,at the mapping regions, may be unknown. According to a furtherembodiment, the system according to the disclosed technique determinesthe pose of the detector relative to the coordinate system by opticallytracking the pose (i.e., location or orientation or both) of thedetector. According to another alternative, the magnetic field detectoris placed in known poses relative to the reference coordinate system.The processor estimates the poses of the detector relative to themagnetic coordinate system. Alternatively, the poses of the detector,relative to the reference coordinate system, at the mapping regions, maybe partially known. For example, when only the locations of the detectorare known, then, the system according to the disclosed techniquedetermines only the orientations of the detector in the referencecoordinate system. When only the orientations of the detector are known,then, the system according to the disclosed technique determines onlythe locations of the detector in the reference coordinate system.

According to another embodiment of the disclosed technique, at least oneadditional tracking system (e.g. an optical tracker, an inertialtracker, an ultrasound tracker, mechanical tracker or any combinationthereof), provides additional information relating to the pose of themapping handle and thus of the magnetic field detector. This additionalinformation may be employed as constraints when estimating theparameters characterizing the magnetic field model. The additionaltracking system determines information relating to the pose of themagnetic field detector at a portion of the magnetic field fluxmeasurements. Thus, a portion of the magnetic field flux measurementsare associated with respective pose related information. The poserelated information, respective of the portion of magnetic field fluxmeasurement may include information relating to only the selected poserelated parameters (i.e., selected location coordinates or selectedorientation angles or a selected combination of location coordinates andorientation angles) at each of the portion or magnetic field fluxmeasurements. Additionally or alternatively, the information relating tothe pose of the magnetic field flux measurement may include informationrelating to a set of locations or a set of orientations or a set ofcombinations of location and orientation. Furthermore, each selectedmagnetic field flux measurement may be associated with differentrespective pose related information. For example, one measurement isassociated only with location while another measurement is associatedonly with orientation. The system estimates the magnetic field modelaccording to the magnetic field flux measurements and the poses relatedinformation respective of the portion of magnetic field fluxmeasurements. It is noted that the magnetic field flux measurements withno respective pose related information or with partial respective poserelated information are also employed when estimating the magnetic fieldmodel. Furthermore, no prior knowledge regarding the magnetic fieldmodel is required only of a magnetic field model template.

Reference is now made to FIG. 1, which is a schematic illustration of asystem, generally referenced 100, for mapping a magnetic field in avolume of interest, constructed and operative in accordance with anembodiment of the disclosed technique. System 100 includes a magneticfield transmitter 102, a magnetic field detector 104, a freestandingmapping handle 106, a memory 107 and a processor 108. Magnetic fieldtransmitter 102 includes one or more (e.g., three) magnetic fieldgenerators (e.g., coils with electric current flowing there through—notshown). Each magnetic field generator generates a magnetic field whichis uniquely identifiable (e.g., each magnetic field has a uniquefrequency and the fields are transmitted at substantially the same timeor, each magnetic field is generated at a different time). Magneticfield detector 104 includes one or more (e.g., three) magnetic fieldsensors (e.g., coils with electric current induced therein, hall-effectsensors). In general, for the purpose of mapping a magnetic field, thenumber of magnetic field sensors in the magnetic field detector timesthe number of magnetic field generators in the magnetic fieldtransmitter must be larger than the number of degrees of freedomrequired to track the object. For example, for six degrees of freedom,three for location and three for orientation, the number of magneticfield sensors in magnetic field detector 104, times the number ofmagnetic field generators in magnetic field transmitter 102, must belarger than six (e.g., nine). Thus, system 100 acquires additionalinformation relating to the deviations between the magnetic field fluxpredicted by the magnetic field model, and the magnetic field fluxmeasured by magnetic field detector 104. This information is related tothe parameters of the magnetic field model. For example, when employingthree sensors and three magnetic field transmitters, there are moregenerator detector pairs than there are pose parameters, which define anover-determined set of equations (i.e., there are more equations thanthere are unknown). Furthermore, the known relative orientation betweenthe magnetic field sensors introduces additional constraints on thedetermined pose of magnetic field detector 104 during the mappingprocess. These constraints are introduced to the set of equations whenestimating the magnetic field model.

Processor 108 is coupled with memory 107 and with magnetic fielddetector 104. Processor 108 is, optionally, further coupled withmagnetic field transmitter 102 (i.e., magnetic field transmitter 102 mayoperate independently of processor 108). When processor 108 is notcoupled with magnetic field transmitter 102, then processor 108 requiresinformation regarding the operation of magnetic field transmitter 102(e.g., transmission frequency, transmission power, duty cycle and thelike). Magnetic field detector 104 is firmly coupled with freestandingmapping handle 106. Thus, magnetic field detector 104 is alsofreestanding. Magnetic field transmitter 102, and thus magnetic field110 are associated with a magnetic coordinate system 112. Memory 107stores a magnetic field model. Volume of interest 118 is associated witha reference coordinate system 114.

Magnetic field transmitter 102 generates a magnetic field 110 toward avolume of interest 118. An operator 116 holds freestanding mappinghandle 106 in her hand. Operator 116 freely moves freestanding mappinghandle 106 (i.e., the trajectory of the mapping handle 106, from onepose in the volume of interest to another pose in the volume ofinterest, has no constraints thereupon) through volume of interest 118,to acquire a sufficient amount of samples, for a required degree ofaccuracy of the magnetic field model. Thus, magnetic field detector 104freely moves within volume of interest 118 at a random trajectory 120.When operator 116 freely moves freestanding mapping handle 106 throughvolume of interest 118, magnetic field detector 104 measures themagnetic flux at a plurality of poses 122 ₁-122 _(N) (i.e., either aplurality of locations or a plurality of orientation or both) and storesthese measurements in memory 107. Processor 108 determines the magneticfield vectors corresponding to each of poses 122 ₁-122 _(N), accordingto the measurements of the magnetic field flux. Processor 108, estimatesposes 122 ₁-122 _(N) of magnetic field detector 104 relative to magneticcoordinate system 112, according to the determined correspondingmagnetic field vectors.

When no previous model of the magnetic field exists, processor 108estimates poses 122 ₁-122 _(N) relative to magnetic coordinate system112, according to a generic model of magnetic field 110 (e.g., a modelof one or more magnetic dipoles with guessed or heuristically determinedparameters) stored in memory 107. Processor 108 uses these poseestimations to estimate the parameters characterizing the magnetic fieldmodel of magnetic field 110. Processor 108 estimates the parameterscharacterizing the magnetic field model according to deviations betweenthe measurements of the magnetic field flux and predictions of themagnetic field flux, at the estimated poses, determined according to thestored magnetic field model (i.e., either the generic model or apreviously estimated magnetic field that is stored in memory 107). Thus,processor 108 estimates a new magnetic field model and stores this newmodel in memory 107 instead of the previous model. Processor 108 may usethe new estimated magnetic field model to re-estimate the poses 122₁-122 _(N) (i.e., relative to magnetic coordinate system 112) ofmagnetic field detector 104 and use these re-estimated poses tore-estimate the parameters characterizing the magnetic field model.Processor 108 may repeat this iterative process for a predeterminednumber of times or until a desired degree of accuracy is achieved.Processor 108 stores the estimated parameters in memory 107. Estimatingthe parameters of a magnetic field model is further explained hereinbelow, in conjunction with FIG. 7. Furthermore, processor 108 registersmagnetic coordinate system 112 with a reference coordinate system 114.Thus, each pose (i.e., location or orientation or both) in magneticcoordinate system 112 has a corresponding pose in reference coordinatesystem 114. Registering a magnetic coordinate system with a referencecoordinate system is further explained in conjunction with FIG. 4.

Alternatively, processor 108 estimates the magnetic field modelaccording to deviations between the values of parameters measured ineach sensor or magnetic field detector (e.g., the amplitude, frequencyand phase of the magnetic field) and the values of the same parameterspredicted by magnetic field model stored in memory 107. It is noted thatprocessor 108 does not necessarily estimates the pose of magnetic fielddetector 104 according to the model, only the relevant parameters.

According to another embodiment, the system according to the disclosedtechnique guides the operator through a plurality of mapping regionswithin the volume of interest. The system may guide the operator, forexample, by audio signals (e.g., sounds corresponding to directions,synthesized words). The system may guide the operator visually (e.g., adisplay displaying representations of the mapping regions and thefreestanding mapping handle thereon or by displaying arrows directing anoperator to move the mapping handle in a selected direction).

Reference is now made to FIG. 2, which is a schematic illustration of asystem, generally referenced 150, for mapping a magnetic field in avolume of interest, constructed and operative in accordance with anotherembodiment of the disclosed technique. System 150 includes a magneticfield transmitter 152, a magnetic field detector 154, a freestandingmapping handle 156, a processor 158, a memory 157 and a guide 160.Magnetic field transmitter 152 includes one or more (e.g., three)magnetic field generators (e.g., coils with electric current flowingthere through—not shown). Each magnetic field generator generates amagnetic field which is uniquely identifiable (e.g., each magnetic fieldhas a unique frequency or each magnetic field is generated at adifferent time). Magnetic field detector 154 includes one or more (e.g.,three) magnetic field sensors (e.g., coils with electric current inducedtherein, hall-effect sensors). For the purpose of mapping a magneticfield, the number of magnetic field sensors in magnetic field detector154 times the number of magnetic field generators in magnetic fieldtransmitter 152 must be larger than the number of degrees of freedomrequired for tracking the object. Guide 160 may be a loudspeakersounding audio signals or a display displaying representations of thevolume of interest 170 and freestanding mapping handle 156 (e.g., a twodimensional or a three dimensional representation).

Processor 158 is coupled with magnetic field detector 154, with memory157 and with guide 160. Processor 158 is, optionally, further coupledwith magnetic field transmitter 152 (i.e., magnetic field transmitter152 may operate independently of processor 158). When processor 158 isnot coupled with magnetic field transmitter 152, then processor 158requires information regarding the operation of magnetic fieldtransmitter 152 (e.g., transmission frequency, transmission power, dutycycle and the like). Magnetic field detector 154 is firmly coupled withfreestanding mapping handle 156. Thus, magnetic field detector 154 isalso freestanding. Magnetic field transmitter 152, and thus magneticfield 162 are associated with a magnetic coordinate system 164. Memory157 stores a magnetic field model. Volume of interest 170 is associatedwith a volume coordinate system 166.

Magnetic field transmitter 152 generates a magnetic field 162 towardvolume of interest 170. An operator 168 holds freestanding mappinghandle 156 in his hand. Guide 160 guides the operator 168 to freely movemapping handle 156 (i.e., the trajectory of the mapping handle 156, fromone pose in the volume of interest to another pose in the volume ofinterest, has no constraints thereupon). Thus, magnetic field detector154 also freely moves within volume of interest 170 through mappingregions 172 ₁-172 _(R). Guide 160 guides the operator 168 to freely movefreestanding mapping handle 156 at least until magnetic field detector154 has moved through all the mapping regions 172 ₁-172 _(R). Guide 160guides operator 168, for example, by sounding audio signalscorresponding to directions, or sounding synthesized words.Alternatively, guide 160 guides operator 168 visually. For example,guide 160 is a display (e.g., a two dimensional display or a threedimensional display) displaying representations of the mapping regions172 ₁-172 _(R), or a pose related thereto, and freestanding mappinghandle 156 thereon. The representations of mapping regions 172 ₁-172_(R) may be deleted from the display, or otherwise marked, when magneticfield detector 154 passes there through. Alternatively, guide 160displays arrows directing operator 168 to move freestanding mappinghandle 156 toward a selected direction.

Magnetic field detector 154 measures the magnetic field vectors at aplurality of regions 172 ₁-172 _(R) and stores these measurements inmemory 157. As described above, in conjunction with FIG. 1, magneticfield detector 154 measures the magnetic flux at a plurality of pose ofmagnetic field detector 154 in regions 172 ₁-172 _(R). Processor 158determines the magnetic field vectors corresponding to each pose ofmagnetic field detector 154, according to the measurements of themagnetic field flux. Processor 158 estimates the poses of magnetic fielddetector 154, relative to magnetic coordinate system 164, according tothe determined corresponding magnetic field vectors.

When no previous model of the magnetic field exists, processor 158estimates the poses of magnetic field detector 154 relative to magneticcoordinate system 164, according to a generic model of magnetic field162 stored in memory 157. Processor 158 uses these pose estimations toestimate the parameters characterizing the magnetic field model ofmagnetic field 162. Processor 158 estimates the parameterscharacterizing the magnetic field model according to deviations betweenthe measurements of the magnetic field flux and predictions of themagnetic field flux, at the estimated poses, determined according to thestored magnetic field model (i.e., the magnetic field that is stored inmemory 157). Thus, processor 158 estimates a new magnetic field modeland stores this new model in memory 157 instead of the previous model.Processor 158 may use the new estimated magnetic field model tore-estimate the poses (i.e., relative to magnetic coordinate system 164)of magnetic field detector 154 and uses these re-estimated poses tore-estimate the parameters characterizing the magnetic field model.Processor 158 may repeat this iterative process for a predeterminednumber of times or until a desired degree of accuracy is achieved.Processor 158 stores the estimated parameters in memory 157.

The freestanding mapping handle may be coupled with a mechanical arminstead of being hand held by an operator. The mechanical arm is capableof freely moving through a plurality of poses within the volume ofinterest (i.e., the trajectory of the mechanical arm from one pose inthe volume of interest to another pose in the volume of interest has noconstraints thereupon). Accordingly, the mechanical arm either movesrandomly through a plurality of poses within the volume of interest orguide through a plurality of regions of interest within the volume ofinterest.

Reference is now made to FIG. 3, which is a schematic illustration of asystem, generally reference 200, constructed and operative in accordancewith a further embodiment of the disclosed technique. System 200includes a magnetic field transmitter 202, a magnetic field detector204, a mapping handle 206, a mechanical arm 208, a mechanical arminterface 210, a memory 212, and a processor 214. Magnetic fieldtransmitter 202 includes one ore more (e.g., three) magnetic fieldgenerators (e.g., three coils with electric current flowing therethrough—not shown). Each magnetic field generator generates a magneticfield which is uniquely identifiable (e.g., each magnetic field has aunique frequency or each magnetic field is generated at a differenttime). Magnetic field detector 204 includes one or more (e.g., three)magnetic field sensors (e.g., coils with electric current inducedtherein, hall-effect sensors). For the purpose of mapping a magneticfield, the number of magnetic field sensors in magnetic field detector204 times the number of magnetic field generators in the magnetic fieldtransmitter 202 must be larger than the number of degrees of freedomrequired for tracking the object.

Processor 214 is coupled with memory 212, with magnetic field detector204, and with mechanical arm interface 210. Processor 214 is,optionally, further coupled with magnetic field transmitter 202 (i.e.,magnetic field transmitter 202 may operate independently of processor214. When processor 214 is not coupled with magnetic field transmitter202 then processor 214 requires information regarding the operation ofmagnetic field transmitter 202 (e.g., transmission frequency,transmission power, duty cycle and the like). Magnetic field detector204 is coupled with mapping handle 206. Mapping handle 206 is coupledwith mechanical arm 208. Mechanical arm 208 is coupled with mechanicalarm interface 210. Mechanical arm 208 includes a plurality of actuator(not shown) enabling mechanical arm 208 to freely move to a plurality ofposes (i.e., locations or orientations or both) within a volume ofinterest 216. Since mechanical arm 208 freely moves within volume ofinterest 216 mapping handle 206 and thus magnetic field detector 204 isfreestanding. Magnetic field transmitter 202, and thus magnetic field218 are associated with a magnetic coordinate system 220. Memory 212stores a magnetic field model. Volume of interest 216 is associated witha volume coordinate system 222.

Magnetic field transmitter 202 generates a magnetic field 218 towardvolume of interest 216. Processor 214 directs mechanical arm interface210 to freely move mechanical arm 208 (i.e., the trajectory of themechanical arm 208 from one pose in the volume of interest to anotherpose in the volume of interest has no constraints thereupon) withinvolume of interest 216 either randomly or to a plurality of regions ofinterest. Magnetic field detector 204 measures the magnetic flux at aplurality of poses. As described above, in conjunction with FIGS. 1 and2, processor 214 iteratively estimates the parameters of the magneticfield model by estimating the poses of magnetic field detector 204 andusing the poses estimations to estimate the parameters of the magneticfield model. Processor 214 may repeat this iterative process for apredetermined number of times or until a desired degree of accuracy isachieved. Processor 214 stores the estimated parameters in memory 212.It is noted that mechanical arm 208 is brought herein as an example. Ingenerally, any mechanical support capable of moving through a pluralityof poses in the volume of interest is suitable. It is noted thatmechanical arm 208 may be replaced with any mechanical support capableof moving to a plurality of poses within volume of interest 216. Forexample, magnetic field detector 204 may be coupled with gimbals,mounted on tracks, capable of rotating in three dimensions and capableof moving in three dimensions.

When a magnetic tracking system according to the disclosed techniquetracks the pose of an object in a reference coordinate system (e.g., thecoordinate system associated with a cockpit of an aircraft or thecoordinate system of an image), the system registers the magneticcoordinate system with the reference coordinate system. In other words,the system determines a correspondence between the poses (i.e., locationor orientation or both) relative to the magnetic coordinate system andthe poses relative to the reference coordinate system. Thus each posedetermined by the magnetic tracking system, relative to the magneticcoordinate system, has a corresponding pose relative to the referencecoordinate system. The system may register the magnetic coordinatesystem with a reference coordinate system for example, by placing themagnetic field detector at a known pose, relative to the referencecoordinate system, and determine the pose of the magnetic field detectorrelative to the magnetic coordinate system. Alternatively, when the poseof the magnetic field transmitter, relative to the reference coordinatesystem, is known, each pose relative to the magnetic coordinate systemis associated with a respective pose relative to the referencecoordinate system. Thus, each determined pose of transmitter in themagnetic coordinate system has an associated pose in the referencecoordinate system.

According to another embodiment of the disclosed technique, an imager isaffixed on the freestanding mapping handle. The camera acquires at leastone image of articles having known poses relative to the referencecoordinate system. The processor estimates the pose (i.e., as mentionedabove, either location or orientation or both) of the magnetic fielddetector relative to the magnetic coordinate system and the pose of thecamera relative to the reference coordinate system. Since the spatialrelationship between the camera and the magnetic field detector isknown, the processor determines the correspondence between the referencecoordinate system and the magnetic coordinate system.

Reference is now made to FIG. 4, which is a schematic illustration of asystem, generally referenced 250, for mapping a magnetic field in avolume of interest, constructed and operative in accordance with anotherembodiment of the disclosed technique. System 250 includes a magneticfield transmitter 252, a first magnetic field detector 254, a secondmagnetic field detector 255, a freestanding mapping handle 256, a memory257, an imager 258, and a processor 260. System 250 may further includea guide (not shown) similar to the guide 160 described hereinaboveconjunction with FIG. 2. Magnetic field transmitter 252 include one oremore (e.g., three) magnetic field generators (e.g., coils with electriccurrent flowing there through—not shown). Each magnetic field generatorgenerates a magnetic field which is uniquely identifiable (e.g., eachmagnetic field has a unique frequency or each magnetic field isgenerated at a different time). Each of First magnetic field detector254 and second magnetic field detector 255 include one or more (e.g.,three) magnetic field sensors (e.g., coils with electric current inducedtherein, hall-effect sensors). As mentioned above, for the purpose ofmapping a magnetic field, the total number of magnetic field sensors infirst magnetic field detector 254 and second magnetic field detector255, times the number of magnetic field generators in magnetic fieldtransmitter 252, must be larger than the number of degrees of freedomrequired for tracking the object. Imager 258 may be a camera operating,for example, in the Infrared (IR) spectrum or in the visual spectrum orany other desired spectrum. Imager 258 may further be a medical imager(e.g., X-ray). The spatial relationship (i.e., the relative pose),between first magnetic field detector 254 and second magnetic fielddetector 255, is known and stored in memory 207.

Processor 260 is coupled with first magnetic field detector 254 and withsecond magnetic field detector 254, with memory 257 and with imager 258.Processor 260 is, optionally, further coupled with magnetic fieldtransmitter 252 (i.e., magnetic field transmitter 252 may operateindependently of processor 260). When system 250 includes a guide, theguide is also coupled with processor 260. First magnetic field detector254, second magnetic field detector 255 and camera 258 are firmlycoupled with freestanding mapping handle 256. Thus, first magnetic fielddetector 254, second magnetic field detector 255 and imager 258 are alsofreestanding. Magnetic field transmitter 252, and thus magnetic field262 are associated with a magnetic coordinate system 264. Memory 257stores a magnetic field model. Volume of interest 268 is associated witha reference coordinate system 266.

Magnetic field transmitter 252 generates a magnetic field 262 toward avolume of interest 268. An operator (not shown) holds freestandingmapping handle 256 in her hand. The operator freely moves freestandingmapping handle 256 (i.e., the trajectory of the mapping handle 256, fromone pose in the volume of interest to another pose in the volume ofinterest, has no constraints thereupon), and thus first magnetic fielddetector 254, second magnetic field detector 255 and imager 258 withinvolume of interest 268. First magnetic field detector 254 and secondmagnetic field detector 255 measure the magnetic flux at a plurality ofposes (i.e., locations or orientations or both). Processor 260determines the magnetic field vector corresponding to each poseaccording to the measurements of the magnetic field flux. Processor 260estimates the poses of first magnetic field 254 and second magneticfield detector 255, relative to magnetic coordinate system 264,according to the determined corresponding magnetic field vectors. Thus,processor 260 estimates the pose of mapping handle 256 and consequentlyof imager 258. Since the spatial relationship between first magneticfield detector 254 and second magnetic field 255 is known, the poseestimates of first magnetic field detector 254 and second magnetic fielddetector 255 must comply (i.e., within a determined degree of accuracy)with the known relative pose, between first magnetic field detector 254and second magnetic field detector 255 (i.e. due to the firm coupling offirst magnetic field detector 254 and second magnetic field detector 255with freestanding mapping handle 256). In other words, the knownrelative pose, between first magnetic field detector 254 and secondmagnetic field detector 255, introduces constraints to the poseestimations thereof. These added constraints improve the accuracy of theestimated poses. Processor 260 estimates the parameters characterizingthe magnetic field model. Processor 260 stores the estimated parametersin memory 257.

When no previous model of the magnetic field exist, processor 260estimates the poses of first magnetic field detector 254 and secondmagnetic field detector 255 relative to magnetic coordinate system 264,according to a generic model of magnetic field 262 (e.g., a model of oneor more magnetic dipoles) stored in memory 257. Processor 260 uses thesepose estimations to estimate the parameters characterizing the magneticfield model of magnetic field 262. Processor 260 estimates theparameters characterizing the magnetic field model according todeviations between the measurements of the magnetic field flux andpredictions of the magnetic field flux, at the estimated poses (i.e.,locations or orientations or both), determined according to the storedmagnetic field model (i.e., the magnetic field that is stored in memory257). Thus, processor 260 estimates a new magnetic field model andstores this new model in memory 257 instead of the previous model.Processor 260 may use the new estimated magnetic field model tore-estimate the poses of first magnetic field detector 254 and secondmagnetic field detector 255 (i.e., relative to magnetic coordinatesystem 264) and use these re-estimated poses to re-estimate theparameters characterizing the magnetic field model. Processor 260 mayrepeat this iterative process for a predetermined number of times oruntil a desired degree of accuracy is achieved. Processor 260 stores theestimated parameters in memory 257.

Prior, during or after the estimation of the magnetic field model,imager 258 acquires an image of articles 270 ₁, 270 ₂, 270 ₃, 270 ₄, 270₅ and 270 ₆ and provides this acquired image to processor 260. Memory257 stores the poses of articles 270 ₁-270 ₆, relative to referencecoordinate system 266. Processor 260 determines the pose of imager 258and thus, the pose of mapping handle 256, first magnetic field detector254 and second magnetic field detector 256, relative to referencecoordinate system 266, according to the acquired image of articles 270₁-270 ₆ (i.e., since imager 258, first magnetic field detector 254 andsecond magnetic field detector 256 are all firmly coupled withfreestanding mapping handle 256).

The number of articles 270 ₁-270 ₆ (i.e., six) is brought herein as anexample. It is noted that articles 270 ₁-270 ₆ are optically detectablearticles that may typically exist in volume of interest 268 (e.g.,boresight reference unit placed closed to detectable volume).Alternatively, articles 270 ₁-270 ₆ may be optically detectable articlesspecially placed in volume of interest 268 (e.g., fiducials or LightEmitting Diodes emitting light in the IR or visual spectrums). The termoptically detectable articles relates herein to articles that eitheremit or reflect light in the operating spectrum of imager 258. It isnoted that articles 270 ₁-270 ₆ may exhibit no rotational symmetry orpartial rotational symmetry. Thus, processor 260 can determine theazimuth the elevation and the roll angles of imager 258, relative to thereference coordinate system, according to an image of one article only.

Alternatively, mapping handle 256 may be coupled with a mechanical arm(not shown) such as mechanical arm 208 (FIG. 3). The mechanical arminterface provides processor 260 with information regarding the pose ofthe tip of mechanical arm relative to reference coordinate system 226(e.g., according to the pose of the base of mechanical arm 208 thegeometry of mechanical arm 208 and the state of the actuators ofmechanical arm 208). Thus, processor 260 determines the pose of magneticfield detector 254 relative to reference coordinated system 266.

Magnetic field detector 254 measures the magnetic field flux. Processor260 determines, accordingly, the pose of magnetic field detector 254,relative to magnetic coordinate system 264. Since processor 264determines the pose of magnetic field detector 254 relative to bothreference coordinate system 266 and magnetic coordinate system 264processor 260 therefore, determines the correspondence between referencecoordinate system 266 and magnetic coordinate system 264. Thus,processor 260 registers reference coordinate system 266 with magneticcoordinate system 264.

In general, processor 260 registers the magnetic coordinated system withthe reference coordinate system, by determining the pose (i.e., locationor orientation or both) of the magnetic field detector in the referencecoordinate system. Accordingly, for example, processor 260 determinesthe orientation of magnetic field detectors 254 and 255 in referencecoordinate system 222, according to the following set of equationsrepresented in matrix from:[HRPToDRPPos]·[DRPPos]·[ModelPos]=[HRPPos]  (1)

Equation (1) relates to registration of orientation only. A similarequation may be used for registering the location of first and secondmagnetic field detectors 254 and 255 in reference coordinate system 222.In equation (1), HRPToDRPPos denotes relative pose between a HandleReference Point (HRP, not show) and a Detector Reference Point (DRP,also not shown). HRP is a point on mapping handle 256 according to whichthe pose of mapping handle 256, in reference coordinate system 266, isdetermined. DRP is a point on mapping handle 256 with known relativepose between the DRP and each of first and second magnetic fielddetectors 254 and 255 (i.e., the DRP may be one of magnetic fielddetectors 254 or 255 since the relative pose between magnetic fielddetector 254 and 255 is known). DRPPos denotes the pose of the DRP inmagnetic coordinate system 264 and is determined according to themeasurements made by first and second magnetic field detectors 254 and255. ModelPos denotes the transformation between magnetic coordinatesystem 264 and the reference coordinate system 266. HRPPos denotes thepose of the HRP in reference coordinate system 266 and is determinedaccording to the images acquired by imager 258. The symbol ‘·’ denotesmatrix multiplication.

Processor 256 determines HRPPos according to images of articles 270 ₁,270 ₂, 270 ₃, 270 ₄, 270 ₅, 270 ₆, (i.e., located in volume of interest266), acquired by imager 258. Imager 258 is affixed to the mappinghandle at a known relative pose to the HRP. Alternatively, imager 258may be affixed in volume of interest 268. Thus, the pose of imager 258in reference coordinate system 222 is also known. Processor 256determines HRPPos according to images, acquired by imager 258, ofarticles (not shown) located on mapping handle 256 with a known relativepose to the HRP. The articles on mapping handle 256 are opticallydetectable articles that may typically exist on mapping handle 256(e.g., the tip thereof). Alternatively, the articles on mapping handle256 may be optically detectable articles specially placed on mappinghandle 256 (e.g., fiducials or Light Emitting Diodes—LEDs).

When HRPToDRPPos is known, processor 260 determines ModelPos only (i.e.,since HRPPos is determined according to the images acquired by theimager), and only one article is needed (i.e. this article exhibits norotational symmetry or partial rotational symmetry such as a crosshair,enabling processor 260 to determine the three orientation angles). WhenHRPToDRPPos is unknown, processor 260 determines HRPToDRPPos as well anda minimum of three articles are needed. In general, Equation (1) is anon-linear set of equations which can be solved, for example, accordingto the Newton-Raphson Method.

Reference is now made to FIG. 5A which is a schematic illustration of amapping handle, generally reference 300 and a magnetic field detector,generally referenced 302, constructed and operative in accordance withanother embodiment of the disclosed technique. Magnetic field detector302 includes one magnetic field sensor 304 (e.g., a coil). Magneticfield detector 302 is coupled with mapping handle 300. As mentionedabove, in general, the number of magnetic field generators times thenumber of sensors should be larger than the number of required locationand orientation parameters. Therefore, to map the magnetic field anddetermine the parameters of a magnetic field model, used to determineboth location and orientation of a tracked object, a magnetic fieldtransmitter which includes at least seven magnetic field generators isrequired. Thus, there are more generator detector pairs than there arepose parameters, which define an over-determined set of equations (i.e.,there are more equations than there are unknowns). Therefore, this setof equations includes additional information relating to the deviationsbetween the magnetic field predicted by the magnetic field model and themagnetic field measured by magnetic field detector 302.

Reference is now made to FIG. 5B which is a schematic illustration of amapping handle, generally reference 310 and a magnetic field detector,generally referenced 312, constructed and operative in accordance with afurther embodiment of the disclosed technique. Magnetic field detector312 includes two magnetic field sensors 314 and 316. Magnetic fielddetector 312 is coupled with mapping handle 310. To map the magneticfield and determine the parameters of a magnetic field model a magneticfield transmitter which employs at least four magnetic field generatorsis required. Thus, there are more generator detector pairs than thereare pose parameters, which define an over-determined set of equations(i.e., there are more equations than there are unknown). Therefore, thisset of equations includes additional information relating to thedeviations between the magnetic field predicted by the magnetic fieldmodel and the magnetic field measured by magnetic field detector 312.

Reference is now made to FIG. 5C which is a schematic illustration of amapping handle, generally reference 320 and a magnetic field detector,generally referenced 322, constructed and operative in accordance with afurther embodiment of the disclosed technique. Magnetic field detector322 includes three magnetic field sensors 324, 326 and 328. Magneticfield detector 322 is coupled with mapping handle 320. To map themagnetic field and determine the parameters of a magnetic field model amagnetic field transmitter which employs at least three magnetic fieldgenerators is required. Thus, there are more generator detector pairsthan there are pose parameters, which define an over-determined set ofequations (i.e., there are more equations than there are unknown).Therefore, this set of equations includes additional informationrelating to the deviations between the magnetic field predicted by themagnetic field model and the magnetic field measured by magnetic fielddetector 322. Furthermore, the known relative orientation betweenmagnetic field sensor 324, 326 and 328 introduces additional constraintsto the determined pose of magnetic field detector 322 during the mappingprocess. Thus, three transmitters and two of the sensors (e.g., sensor324 and sensor 326) may be employed for determining the pose of detector322 and thus of sensor 328. These deviations may be employed to updatethe parameters of the magnetic field model.

Reference is now made to FIG. 5D which is a schematic illustration of amapping handle, generally reference 330 and two magnetic field detector,generally referenced 332 and 334, constructed and operative inaccordance with another embodiment of the disclosed technique. Each ofmagnetic field detectors 332 and 334 include one magnetic field sensor336 and 338 respectively. Each of magnetic field detectors 335 and 334is coupled with mapping handle 300. The spatial relationship (i.e., therelative location and orientation), between magnetic field detector 332and magnetic field detector 334, is known. Therefore, to map themagnetic field and determine the parameters of a magnetic field model amagnetic field transmitter which employs at least four magnetic fieldgenerators are required. Thus, there are more generator detector pairsthan there are pose parameters, which define an over-determined set ofequations (i.e., there are more equations than there are unknown).Therefore, this set of equations includes additional informationrelating to the deviations between the magnetic field predicted by themagnetic field model and the magnetic field measured by magnetic fielddetectors 332 and 334. Furthermore, the known spatial relationship(i.e., relative location and orientation) between magnetic fielddetectors 332 and 334 introduces additional constraints on thedetermined poses of magnetic field detectors 332 and 334 during themapping process. These constraints may be employed to update theparameters of the magnetic field model.

Reference is now made to FIG. 5E which is a schematic illustration of amapping handle, generally reference 340 and two magnetic fielddetectors, generally referenced 342 and 344, constructed and operativein accordance with another embodiment of the disclosed technique. Eachof magnetic field detectors 342 and 344 include three magnetic fieldsensors. Magnetic field detector 342 includes magnetic field sensors346,348 and 350. Magnetic field detector 344 includes magnetic fieldsensors 352, 356 and 354. Each of magnetic field detectors 342 and 344is coupled with mapping handle 340. The spatial relationship (i.e., therelative location and orientation), between magnetic field detector 342and magnetic field detector 344, is known. To map the magnetic field anddetermine the parameters of a magnetic field model a magnetic fieldtransmitter which employs at least two magnetic field generators isrequired. Thus, there are more generator detector pairs than there arepose parameters, which define an over-determined set of equations (i.e.,there are more equations than there are unknown). Therefore, this set ofequations includes additional information relating to the deviationsbetween the magnetic field predicted by the magnetic field model and themagnetic field measured by magnetic field detectors 342 and 344.Furthermore, the known spatial relationship between magnetic fielddetectors 342 and 344 introduces additional constraints on thedetermined poses of magnetic field detectors 342 and 344 during themapping process. These constraints may be employed to update theparameters of the magnetic field model.

Reference is now made to FIG. 6, which is a schematic illustration of amethod for mapping a magnetic field in accordance with anotherembodiment of the disclosed technique. In procedure 400, a volume ofinterest is determined. The volume of interest is associated with areference coordinate system. For example, the volume of interest is acockpit of an aircraft. The volume of interest may further be the bodyof a patient or a room.

In procedure 402, a magnetic field models is determined. The magneticfield model is associated with a magnetic coordinate system. This modelmay be a physical model or a mathematical model. The magnetic fieldmodel includes parameters characterizing the model. In general, when themodel is a physical model, the parameters are physical parameters of themagnetic field. With reference to FIG. 1, memory 107, stores theparameters characterizing the determined magnetic field model.

In procedure 404, magnetic field detectors are freely moved within thedetermined volume of interest. The magnetic field detectors may be movedin the volume of interest at a random trajectory. Alternatively, themagnetic field detectors may be freely guided towards regions ofinterest within the volume of interest. With reference to FIG. 1,operator 116 freely moves first magnetic field detector 104 and secondmagnetic field detector 104 within volume of interest 118 in a randomtrajectory 120. With reference to FIG. 2, guide 160 guides operator 168to freely move magnetic field detector 154 through regions of interest172 ₁-172 _(R). With reference to FIG. 3, mechanical arm interface 210directs mechanical arm 208 to freely move within volume of interestseither at a random trajectory or through a plurality of regions ofinterest.

In procedure 406, measurements of the magnetic field flux, at aplurality of poses in the volume of interest, are acquired. When themagnetic field detector is moved in a random trajectory in the volume ofinterest, then, the measurements of the magnetic field flux are acquiredat a plurality of poses on the random trajectory. When the magneticfield detector is guided toward regions of interest in the volume ofinterest, then, the measurements of the magnetic field flux are acquiredat a plurality of poses in the regions of interest. With reference toFIG. 1, magnetic field detector 104 acquires measurements of themagnetic field flux at a plurality of poses 122 ₁-122 _(N) on trajectory120. With reference to FIG. 2, magnetic field detector 154 acquiresmeasurements of the magnetic field flux at a plurality of poses inregions 172 ₁-172 _(R).

In procedure 408 the magnetic field coordinate system is registered withthe reference coordinate system. Reference coordinate system isregistered with the magnetic coordinate system by optically determiningthe pose (i.e., location or orientation or both) of a magnetic fielddetector relative to the reference coordinate system and determining thepose of the magnetic field detector relative to the magnetic coordinatesystem. When the location of the magnetic field transmitter, in thereference coordinate system is known, reference coordinate system isregistered with the magnetic coordinate system by optically determiningthe orientation of a magnetic field detector in the reference coordinatesystem. It is noted that registering the magnetic field coordinatesystem with the reference coordinate system may be performed eitherprior, during or after the procedure of acquiring measurements of themagnetic field flux. When using the poses determined according to theimagers acquired by the imager as constraint on the poses determinedaccording to the measurements of the magnetic field detector, then, theimager acquires the images before the magnetic field model estimation.With reference to FIG. 4, processor 260 determines the pose of firstmagnetic field detector 254 and second magnetic field detector 255relative to magnetic coordinate system 264 according to the measurementsof the magnetic flux in first magnetic field detector 254 and secondmagnetic field detector 255. Processor 260 determines the pose of firstmagnetic field detector 254 and second magnetic field detector 255relative to reference coordinate system 266 according to an image ofarticle 270 ₁-270 ₆ acquired by imager 258.

In procedure 410, the parameters characterizing the magnetic field modelare re-estimated according to deviations between the magnetic field fluxpredicted by the magnetic field model and the measurements of themagnetic field flux. The parameters are estimated iteratively as furtherexplained below in conjunction with FIG. 7. It is noted that when themagnetic coordinate system is registered with the reference coordinatesystem the parameters characterizing the magnetic field model areestimated with reference to the reference coordinate system. However,the parameters characterizing the magnetic field model may be estimatedwith reference to the magnetic coordinate system or any other coordinatesystem. The registration between the magnetic or the other coordinatesystem with the reference coordinate system may be performed at a laterstage. It is further noted that, when registration between the referencecoordinate system and the magnetic coordinate system is performed duringthe mapping of the magnetic field, then, the optical pose measurementsmay be used in conjunction with the magnetic field measurements formapping the magnetic field (e.g., as constraints on the pose of themagnetic field detector). With reference to FIG. 1, processor 108estimates the parameters of the magnetic field model according to themeasurements of the magnetic field flux.

In procedure 412, the re-estimated parameters, characterizing themagnetic field model, are stored. Thereby, a re-estimated magnetic fieldmodel is stored instead of the previously stored magnetic field model.With reference to FIG. 1, processor 108 stores the estimated parameterscharacterizing the magnetic field model in memory 107.

As mentioned above parameters characterizing the magnetic field may beiteratively estimated according to deviations between the measurementsof the magnetic field flux and predictions of the magnetic field flux,at the estimated poses. Accordingly, the poses of the magnetic fielddetector are estimated according to an initially stored magnetic fieldmodel. The parameters characterizing the magnetic field model areestimated according to the estimated poses of the magnetic fielddetector. The parameters of the magnetic field may be re-estimated usingthe estimated poses of the magnetic field detector and the previouslyestimated magnetic field model. This process may be repeated for apredetermined number of times or until a desired degree of accuracy isachieved.

Reference is now made to FIG. 7, which is a schematic illustration of anexemplary method for estimating the parameters of a magnetic field, inaccordance with a further embodiment of the disclosed technique. Inprocedure 420, the pose of the magnetic field detector is estimated foreach measurement of magnetic field flux according to the stored magneticfield model. The poses of the magnetic field detector, relative to themagnetic coordinate system, are estimated, for example, by minimizingthe squared differences between the measurements of the magnetic fieldflux and predictions of the magnetic field flux (i.e., predicted by thestored magnetic field model). This is stated mathematically as follows:

$\begin{matrix}{\arg\;{\underset{\overset{\_}{P},\overset{\_}{O}}{Min}\left\lbrack {{\overset{\_}{M}}_{j} - {\overset{\_}{f}\left( {\theta,{\overset{\_}{P}}_{j},{\overset{\_}{O}}_{j}} \right)}} \right\rbrack}^{2}} & (1)\end{matrix}$wherein P _(j) is the location vector at pose j (e.g., pose 122 _(j) inFIG. 1), Ō_(j) is the orientation vector at one of pose j, M _(j) is themeasurement matrix of the magnetic field at pose j, f(θ,P _(j),Ō_(j)) isthe magnetic field model and θ is a set parameters characterizing themodel. f(θ,P _(j),Ō_(j)) determines the dependency between the magneticfield measurements, the parameters (i.e., θ) of the magnetic field modeland the dependency between the magnetic field measurements and the posesof the magnetic field detector. The parameters θ of f(θ,P _(j),Ō_(j))may describe for example, a set of dipoles or coefficients of apolynomial function. Explicit expressions for f(θ,P _(j),Ō_(j)) arederivatives of Maxwell's equations. With reference to FIG. 1, processor108 estimates the pose of mapping handle 106.

In procedure 422, the parameters characterizing the magnetic field modelare re-estimated according to the estimated poses. The parameters of themagnetic field model are estimated according to the deviations betweenthe measurements of the magnetic field flux and predictions of themagnetic field flux, at the estimated poses, for example, by minimizingthe sum of squared differences there between. This is statedmathematically as follows:

$\begin{matrix}{\arg\;\underset{\theta}{Min}{\sum\limits_{j = 1}^{N}\left\lbrack {{\overset{\_}{M}}_{j} - {\overset{\_}{f}\left( {\theta,{\overset{\_}{P}}_{j},{\overset{\_}{O}}_{j}} \right)}} \right\rbrack^{2}}} & (2)\end{matrix}$wherein N is the total number of locations. With reference to FIG. 1,processor 108 re-estimates the parameters of the magnetic field modelaccording to the estimated poses.

In procedure 424, a ‘model compatibility indicator’ is determined. Thismodel compatibility indicator represents the deviations between themagnetic field model and the actual magnetic field in the volume ofinterest. When the model compatibility indicator is larger then adetermined value, designated as ‘MCI’ in FIG. 7, then, the methodreturns to procedure 420. When the model compatibility indicator issmaller or equal to the determined value, then, the estimated parametersstored. One exemplary model compatibility indicator is a cost functionsuch as a Figure of Merit (FOM). This FOM represents, for example, theratio between the difference between the measurements of the magneticfield flux and the prediction of the magnetic field flux according tothe model, and the measurements of the magnetic field flux. Thisexemplary FOM is stated mathematically as follows:

$\begin{matrix}{{F\; O\; M} = \sqrt{\frac{\sum\limits_{j = 1}^{J}{\sum\limits_{i = 1}^{k}\left\lbrack {M_{ji} - {f_{i}\left( {\theta,{\overset{\_}{P}}_{j},{\overset{\_}{O}}_{j}} \right)}} \right\rbrack^{2}}}{\sum\limits_{i = 1}^{k}M_{ji}^{2}}}} & (3)\end{matrix}$wherein k is the number of generator sensor pairs (e.g., in the case ofthree generators and three sensors there are nine generator sensorpairs), J is the number of measurements, M_(ji) is the measurement, atpose j, of the magnetic field generated by one of the generator andsensed by one of the sensors. Furthermore, f_(i)(θ,P _(j),Ō_(j)) is themagnetic field at pose j of the i^(th) generator sensor pair, accordingto the magnetic field model. Another exemplary model compatibilityindicator is the reciprocal of the number of repetition of the method(i.e., how many times the parameters characterizing the magnetic fieldmodel have been re-estimated). Yet another exemplary model compatibilityindicator is the deviations between the poses of the magnetic fielddetector, determined according to the magnetic field model, and theposes of the magnetic field detector determined according to the imagesacquired by the imager. With reference to FIG. 1, processor 108determines a model compatibility indicator of the magnetic field modelfor all poses of magnetic field receiver 104.

Still referring to FIG. 7, it is noted that determining the parametersof the magnetic field model and estimating the pose of the magneticfield detector may be performed simultaneously by, solving a set ofequations which includes all the desired unknowns (i.e., pose parametersand model parameters). It is further noted that if the estimation of theparameters of the magnetic field does not converge, then, a differentmagnetic model having different parameters and coefficients may bedetermined and used.

The systems of FIGS. 1, 2, 3, and 4 are described hereinabove with aconfiguration wherein the magnetic field transmitter is fixed at a knownpose in the volume of interest and the magnetic field detector ismounted on the tracked object. However, it is noted that the systems ofFIGS. 1, 2, 3 and 4 may employ the configuration wherein the magneticfield transmitter is mounted on the mapping handle and the magneticfield detector is fixed at a known pose in the volume of interest.Furthermore, prior knowledge of the volume of interest may provideadditional information regarding the possible orientations of themagnetic field detector. For example, there may be locations in acockpit wherein the magnetic field detector can move only at uniqueorientations. The knowledge of these orientations provides furtherconstraints to the estimated orientations at those locations. As anotherexample, accelerometers may be coupled with the freestanding mappinghandle. These accelerometers provide information regarding the directionand the distance the magnetic field detector traversed between twoconsecutive measurements. The estimated poses, of the magnetic fielddetector, at these two consecutive measurements must be consistent withthe direction and distance determined according to the measurements fromthe accelerometers.

As mentioned hereinabove, a mapping system according to the disclosedtechnique may employ an imager for registering the reference coordinatesystem with the magnetic coordinate system. Further as described above,the system may employ accelerometers to provide constraints on thedetermined pose of magnetic field detector. Also as described above, theoptical pose measurements, determined during registration with thereference coordinate, system may be used in conjunction with themagnetic field measurements for mapping the magnetic field (e.g., asconstraints on the pose of the magnetic field detector).

Generally, a system according to another embodiment of the disclosedtechnique, includes at least one additional tracking system, whichprovides the additional information relating to the pose of thefreestanding mapping handle and thus of the magnetic field detector.This additional tracking system or systems are, for example, an opticaltracker (e.g., imagers with LEDs), Light Detection and Ranging—LIDARsystem, motion capture module (e.g., such as Microsoft's® Kinect®), aninertial tracker, an ultrasound tracker, mechanical tracker or anycombination thereof. The additional information may be employed asconstraints when estimating the parameters characterizing the magneticfield model. For example, the additional tracking system may provideinformation relating only to selected pose parameters. These selectedpose parameters may be selected location coordinates (i.e., either x, yor z or any combination thereof), selected orientation angles (i.e.,either azimuth, elevation or roll or any combination thereof) or aselected combination of location coordinates and orientation angles(e.g., x, elevation and azimuth; y, z and roll; x, y, azimuth andelevation and the like). The selected pose parameters may also relate toall the pose parameters (i.e., x, y, z, azimuth, elevation and roll,also referred to herein as ‘full pose information’). Pose Informationrelating to only a portion or the pose parameters (i.e., not to all thepose parameters) is referred to herein as partial pose information(e.g., x, and azimuth; x, y, z; azimuth elevation and roll).

The additional tracking system determines information relating to thepose of the freestanding mapping handle, and thus of the magnetic fielddetector, for at least a portion of the magnetic field fluxmeasurements. Thus, at least a portion of the magnetic field fluxmeasurements are associated with respective pose related information.The pose related information, respective of the portion of magneticfield flux measurement may include information relating to only theselected pose parameters (i.e., selected location coordinates orselected orientation angles or a selected combination of locationcoordinates and orientation angles). Additionally or alternatively, thepose related information respective of the portion of magnetic fieldflux measurement may include information relating to a set of locationsor a set of orientations or a set of combinations of location andorientation. For example, a set of locations is a line (i.e., in thecoordinate system associated with the additional tracking system) onwhich the magnetic field flux measurement is located. Furthermore, thepose related information respective of each of the portion of magneticfield flux measurement may include different pose parameters. Forexample, one measurement is associated only with location, anothermeasurement is associated only with orientation, yet another measurementis associated with a line on which the measurement was acquired and yetanother measurement is associated with location and orientation.

In general, the total number of acquired measurements should at leastequal the number of unknown parameters of the magnetic field model. Asmentioned above, the information relating to the pose respective of atleast the portion of magnetic field flux measurements is employed asconstraints or a range of constraints (e.g., due to the error of theadditional tracking system) when estimating the parameterscharacterizing the magnetic field model. The system estimates themagnetic field model by iteratively solving a determined orover-determined set of equations, according to the magnetic field fluxmeasurements and the poses related information respective of the portionof magnetic field flux measurements. It is noted that the magnetic fieldflux measurements, with no respective pose related information are alsoemployed when estimating the magnetic field model. For example, theposes of these measurements may also be unknowns to be solved, when asufficient number of measurements with respective pose relatedinformation are acquired. Also, pose parameters, which are not includedin pose related information respective of the portion of magnetic fieldflux measurements, may also be unknowns to be solved. It is noted thatwhen employing an additional tracking system to determine pose relatedinformation of a portion of magnetic field flux measurements, there isno need for the number of magnetic field generator times the number ofmagnetic field sensors to be larger than the number of degrees offreedom required to track the object. Additionally, the system does notrequire any prior knowledge regarding the magnetic field model (i.e.,not even the generic dipole mentioned above in conjunction with FIG. 1and FIG. 4). Rather, only the template of the model (e.g., the type ofthe mathematical function employed for modeling the magnetic field) isknown as further explained below.

Accordingly, a system for mapping a magnetic field in a volume ofinterest according to another embodiment of the disclosed techniqueincludes a magnetic field transmitter which generates a magnetic fieldin a volume of interest and at least one freestanding magnetic fielddetector, operative to freely move within said volume of interest. Theat least one freestanding magnetic field detector acquires measurementsof the flux of said magnetic field at a plurality of poses. The systemfurther includes at least one Pose Information Acquisition Module (PIAM)for measuring information related to the pose of said freestandingmagnetic field detector. This PAIM includes for example light emittersand an imager acquiring images of these light emitters, inertialsensors, ultrasound sensors receiving ultrasound signals from ultrasoundtransmitters, a mechanical tracking module (e.g., mechanical arm), LightDetection and Ranging (LIDAR) module (i.e., a laser and an imager),motion capture module (e.g., Kinect®) and the like. The magnetic fieldmapping system further includes a processor, coupled with the freestanding magnetic field detector and with the at least one PIAM. Theprocessor determines pose related information respective of at least aportion of the measurements according to the information related to thepose of the freestanding magnetic field detector, measured by the atleast one PIAM (i.e., the processor and a PIAM define an additionaltracking system). The processor estimates the entire set of parametersof a magnetic field model template according to the magnetic field fluxmeasurement and the respective poses thereof and incorporates thisentire set of parameters into the magnetic field model template, therebydetermining the magnetic field model. The pose information acquisitionmodel and the processor defining a tracking system. The model includesthe coefficients of the magnetic field model, the order of the magneticfield model, the number of the centers of expansion and the location ofthe centers of expansion of the magnetic field model.

According to the disclosed technique, a single sensor and a singleadditional tracking system, which tracks the pose (i.e., the locationand orientation) of the sensor in the volume of interest, is sufficientfor mapping a magnetic field. Reference is now made to FIG. 8, which isa schematic illustration of a system, generally referenced 500, formapping a magnetic field in a volume of interest, constructed andoperative in accordance with another embodiment of the disclosedtechnique. System 500 includes a magnetic field transmitter 502, amagnetic field detector 504 a freestanding mapping handle 506, a memory508 and a processor 510. System 500 further includes a PAIM, whichincludes an imager 512, and at least one light emitter. The PAIMdepicted in FIG. 8 includes three light emitters 514 ₁, 514 ₂ and 514 ₃.In general, an optical PIAM which includes a single emitter and a singleimager is sufficient to acquire pose related information relating to thepose of magnetic field detector 504 as further explained below.

Magnetic field transmitter 502 includes one or more (e.g., three or six)magnetic field generators (e.g., coils with electric current flowingthere through—not shown). Each magnetic field generator generates amagnetic field which is uniquely identifiable (e.g., each magnetic fieldhas a unique frequency or each magnetic field is generated at adifferent time). Magnetic field detector 504 includes at least onemagnetic field sensor (e.g., a coil with electric current inducedtherein or a hall-effect sensor). It is noted that in system 500, asingle magnetic field sensor is sufficient for mapping the magneticfield. Light emitters 514 ₁, 514 ₂ and 514 ₃ are light source (e.g.,LED) or a light reflector (e.g., ball reflector) which reflects lightincident thereon (i.e., either ambient light, light from various lightsources located at the vicinity of the light reflector or from adedicated light source directing light toward the light reflector).Imager 512 may be a camera operating in a respective spectrum (e.g., inthe IR spectrum or in the visual spectrum or any other desiredspectrum).

Processor 510 is coupled with magnetic field detector 504, with memory508 with imager 512, with light emitters 518 and with light emitters 514₁, 514 ₂ and 514 ₃. Processor 510 is optionally further coupled withmagnetic field transmitter 502 (i.e., magnetic field transmitter 502 mayoperate independently of processor 510). Imager 512, light emitters 514₁, 514 ₂ and 514 ₃ and processor 510 define an optical tracking system.The optical tracking system is associated with an optical coordinatesystem 516.

Magnetic field detector 504 and light emitters 514 ₁, 514 ₂ and 514 ₃are all firmly coupled with freestanding mapping handle 506. Thus,magnetic field detector 504 and light emitters 514 ₁, 514 ₂ and 514 ₃are also freestanding. Furthermore, the spatial relationship (i.e., therelative poses) between light emitters 514 ₁, 514 ₂ and 514 ₃ is known.Also, imager 512 is located at a respective fixed position in referencecoordinate system 516. It is noted that imager 512 need not be withinvolume of interest 518. However, volume of interest 518 should be withinthe Field Of View (FOV) of imager 512. Unlike the magnetic field mappingsystems described hereinabove in conjunction with FIGS. 1-7, for thepurpose of mapping a magnetic field, in system 500, the total number ofmagnetic field sensors in magnetic field detector 504, times the numberof magnetic field generators in magnetic field transmitter 502, need notbe larger than the number of degrees of freedom required for trackingthe object.

Magnetic field transmitter 502 generates a magnetic field 520 toward avolume of interest 518. An operator (not shown) holds freestandingmapping handle 506 in her hand and freely moves freestanding mappinghandle 506. Thus, the operator also freely moves first magnetic fielddetector 504 and light emitters 514 ₁, 514 ₂ and 514 ₃ within volume ofinterest 518. Magnetic field detector 504 measure the magnetic flux at aplurality of poses (i.e., a plurality of locations or orientations orboth). Processor 510 determines the magnetic field vector correspondingto each pose according to the measurements of the magnetic field flux.

Simultaneously to the acquisition of the magnetic field fluxmeasurement, the optical tracking system (i.e., processor 510)determines pose related information respective freestanding mappinghandle 508 and thus respective magnetic field detector 508. Thus, theoptical tracking system determines pose related information (i.e., inoptical coordinate system 516) respective of at least a portion of themagnetic field flux measurements (e.g., since one or more of lightemitters 514 ₁, 514 ₂ and 514 ₃ was obscured from imager 512). Asmentioned above, the pose related information may include informationrelating to only selected pose parameters. Additionally oralternatively, the pose information relating to the portion of magneticfield flux measurements may include information relating to a set oflocation or a set of orientation or a set of combinations of locationand orientation of magnetic field detector 508. Also, the pose relatedinformation of each of the portion of magnetic field flux measurementmay include different pose parameters.

Processor 510 estimates the magnetic field model at least according tothe magnetic field flux measurements and the poses related informationrespective of the portion of magnetic field flux measurements. Processor510 employs the pose related information of the magnetic field fluxmeasurement as constraints or a range of constraints (e.g., due to theerror of the optical tracking system). Processor 510 estimates themagnetic field model by iteratively solving a determined orover-determined set of equations, according to the magnetic field fluxmeasurements and the poses related information respective of the portionof magnetic field flux measurements. Processor 510 may also employ themagnetic field flux measurements with no respective pose relatedinformation when estimating the magnetic field model. For example, poseof these measurements may also be unknowns to be solved, when asufficient number of measurements with respective pose relatedinformation are acquired. Also, pose parameters, which are not includedin pose related information respective of the portion of magnetic fieldflux measurements, may also be unknowns to be solved. Consequently,processor 510 estimates the magnetic field model is estimated in opticalcoordinate system 524. Also, processor 510 does not need any priorknowledge of the magnetic field model. Processor 510 only needs priorknowledge relating to the template of the model, for example, harmonicfunctions (e.g., spherical harmonics, elliptical harmonics, cylindricalharmonics, Fourier series) and the like. Processor 510 estimates notonly the coefficients of the model but also the degree of the model, thelocation of the center of expansion of the model in the opticalcoordinate system 510 and the number of centers of expansion. Thelocation of the center of expansion of the model relates to the locationof the magnetic field generator or generators and to passive magneticfield sources such as metallic objects in which eddy currents areinduced. Furthermore, processor 510 does not need to determine theabsolute pose of each measurement of the magnetic flux. Rather it issufficient for processor 510 to determine the relative pose between thecurrent and the previous measurements of the magnetic flux. It is alsonoted that for determining the order of the model, and the number andlocations of the center of expansions, the poser related informationrespective of at least one of the magnetic field flux measurementsshould include all the location pose parameters (i.e., x, y and z).

Magnetic field mapping system 500 described herein above in conjunctionwith FIG. 8 employs an optical tracking system to provide the poserelated information respective of the portion of magnetic field fluxmeasurements. However, other kinds of tracking systems, which providethe reference poses in a coordinate system associated therewith, withsufficient degree of accuracy, may be employed. For example, the opticaltracking system described in conjunction with FIG. 8 may be replacedwith either an inertial tracking system, an ultrasound tracking systemor a mechanical tracking system, which provides the respective referencelocations and orientation associated with the magnetic field fluxmeasurements. Furthermore, a combination of tracking systems may beemployed for increasing accuracy of the magnetic field mapping systemand providing redundancy and additional functionality thereto as furtherexplained below. In addition, the optical tracking system describedhereinabove in conjunction with FIG. 8 exhibits and an out-inconfiguration (i.e., the imager is stationary and the light emitters aremobile). However, an optical tracking system exhibiting an in-outconfiguration (i.e., the imager is mobile and the light emitters arestationary) or an in-out-out-in configuration (i.e., a mobile imager andmobile light emitters and a stationary imager and stationary lightemitters) may also be employed.

As mentioned above in conjunction with FIG. 8, an optical trackingsystem determines the pose of magnetic field handle 506. To that end,imager 512 acquires an image or images of light emitters 514 ₁, 514 ₂and 514 ₃. The acquired images include information relating to lightemitters 514 ₁, 514 ₂ and 514 ₃. The information relating to lightemitters 514 ₁, 514 ₂ and 514 ₃ is referred to herein as“representations” of the light emitters. These representations may bethe sampled image or images or information relating to objects in theimage associated light emitters 514 ₁, 514 ₂ and 514 ₃. Processor 510determines the pose of freestanding mapping handle 506 relative tooptical coordinate system 516 according to the representations of lightemitters 514 ₁, 514 ₂ and 514 ₃ provided thereto by imager 512.

In general to determine the location and orientation of freestandingmapping handle 506, processor 512 generates and solves at least sixequations with six unknowns (e.g., three unknowns for location, the x, yand z coordinates and three unknowns for orientation, the azimuthelevation and roll angles). A representation of a light emitter isassociated with two angles. For example, when the optical sensor ofimager 512 is a CCD sensor, the CCD sensor is associated with a physicalcenter. An imaginary line passing through this physical center,perpendicular to the sensor plane, defines the optical axis of the CCDsensor. Each pixel in the CCD sensor is associated with a respectivelocation on the CCD sensor, defined by a sensor 2D coordinates system inpixel units (e.g., a pixel located at coordinates [2;3] in the sensor 2Dcoordinates system is the pixel at the intersection of the second colonof pixels with the third row of pixels). Accordingly, each pixel isassociated with a horizontal angle and a vertical angle from the opticalaxis of the sensor, related to the location of the pixel in the sensor2D coordinate system. Consequently, each representation of a lightemitter determined from an image acquired by a CCD sensor is alsoassociated with a respective horizontal angle and a vertical angle fromthe optical axis of the CCD sensor. Thus, the representation associatedwith each of light emitters 514 ₁, 514 ₂ and 514 ₃, determined from theimage acquired by imager 512, is associated with two respective angles.Accordingly a total of six measurements of angles are acquired. Theseangles, along with the known spatial relationship (i.e., relativelocation) between light emitters 514 ₁, 514 ₂ and 514 ₃, define theabove mentioned six equations with six unknowns. Processor 512 solvesthese equations to determine the location and orientation offreestanding mapping handle 506 and thus of magnetic field detector 504.Nevertheless, when, for example, a single light emitter is employed ordetected by the imager, the two angles associated with therepresentation of this single light emitter define a line in thereference coordinate system (e.g., optical coordinate system 516. Asmentioned above, such a line may be employed as pose related informationrespective of a magnetic field flux measurement. When two light emittersare employed or detected by the imager, the two angles associated witheach representation the two light emitters and the known spatialrelationship between these two light emitters provide sufficientinformation to determine four pose parameters in the referencecoordinate system. These four pose parameters may be employed as poserelated information respective of a magnetic field flux measurement.

Reference is now made to FIG. 9, which is a schematic illustration of asystem, generally referenced 550, for mapping a magnetic field in avolume of interest, constructed and operative in accordance with afurther embodiment of the disclosed technique. System 550 includes amagnetic field transmitter 552, a first magnetic field detector 554, asecond magnetic field detector 556, a freestanding mapping handle 558, amemory 560 and a processor 562. System 550 further includes a first PIAMwhich includes a first imager 564, a second imager 566, at least onemoving light emitter 568, at least two fixed light emitters 570 ₁ and570 ₂. System 550 also includes a second PAIM, which includes inertialtracking sensors 572 (e.g., gyro sensors). System 550 may furtherinclude a guide (not shown) similar to the guide 160 describedhereinabove conjunction with FIG. 2.

Magnetic field transmitter 552 includes one or more (e.g., three)magnetic field generators. Each magnetic field generator generates amagnetic field which is uniquely identifiable (e.g., each magnetic fieldhas a unique frequency or each magnetic field is generated at adifferent time). Each one of first magnetic field detector 554 andsecond magnetic field detector 556 include one or more (e.g., three)magnetic field sensors. Either one of at least one moving light emitter566 and at least two fixed light emitters 570 ₁ and 570 ₂ are a lightsource or a light reflector similar to light emitters 514 ₁, 514 ₂ and514 ₃ of FIG. 8. Each one of imager 562 and imager 564 may be a cameraoperating in a respective spectrum (i.e., similar to imager 512 of FIG.8).

Processor 562 is coupled with first magnetic field detector 554 and withsecond magnetic field detector 556, with memory 560, with first imager564, with moving light emitter 568, with second imager 566, with each offixed light emitters 570 ₁ and 570 ₂ and with inertial navigationsensors 572. Processor 562 is optionally further coupled with magneticfield transmitter 552 (i.e., magnetic field transmitter 552 may operateindependently of processor 562). First imager 564, second imager 566,moving light emitter 568, reference light emitters 570 ₁ and 570 ₂ andprocessor 562 define an optical tracking system. Inertial trackingsensors 572 and processor 562 define an inertial tracking system. Theoptical tracking system is associated with an optical coordinate system574. Volume of interest 578 is associated with a reference coordinatesystem 580.

First magnetic field detector 554, second magnetic field detector 556,first imager 564 and moving light emitter 568 are all firmly coupledwith freestanding mapping handle 558. Thus, first magnetic fielddetector 554, second magnetic field detector 556, first imager 564 andmoving light emitter 568 are also freestanding. Furthermore, the spatialrelationship (i.e., the relative pose) first imager 564 and moving lightemitter 568 is known. Also, second imager 566 and fixed light emitters570 ₁ and 570 ₂ are located at a respective fixed position in referencecoordinate system 580 and the spatial relationship therebetween isknown. In FIG. 9, fixed light emitters 570 ₁ and 570 ₂ are depicted asfixedly coupled with second imager 566. It is noted that second imager566 need not be within volume of interest 578. However, volume ofinterest 578 should be within the FOV of second imager 566. Furthermore,fixed light emitters 570 ₁ and 570 ₂ should be within the FOV of firstimager 564. Unlike the systems described herein above in conjunctionwith FIGS. 1-7, and similar to system 500, for the purpose of mapping amagnetic field, the total number of magnetic field sensors in firstmagnetic field detector 554 and second magnetic field detector 556,times the number of magnetic field generators in magnetic fieldtransmitter 558, need not be larger than the number of degrees offreedom required for tracking the object.

Magnetic field transmitter 552 generates a magnetic field 576 toward avolume of interest 578. An operator (not shown) holds freestandingmapping handle 558 in her hand. The operator freely moves freestandingmapping handle 558. Thus, the operator also freely moves first magneticfield detector 554, second magnetic field detector 556, first imager564, moving light emitter 568 and inertial tracking sensors 572 withinvolume of interest 578. First magnetic field detector 554 and secondmagnetic field detector 556 measure the magnetic flux at a plurality ofposes (i.e., a plurality of locations or orientations or both).Processor 564 determines the magnetic field vector corresponding to eachpose according to the measurements of the magnetic field flux.

Simultaneously to the acquisition of the magnetic field fluxmeasurement, the optical tracking system (i.e., processor 564)determines pose related information respective of freestanding mappinghandle 558 in optical coordinate system 580 for at least a first portionof the magnetic field flux measurements. The inertial tracking systemalso determines pose related information respective of freestandingmapping handle 558 in an inertial coordinate system (not shown), for atleast a second portion of the magnetic field flux measurements. It isnoted that the first portion of magnetic field flux measurements and thesecond portion of magnetic field flux measurements may be mutuallyexclusive, partially overlap or completely overlap (i.e., the twoportions are one and the same). When the inertial coordinate system isregistered with optical coordinate system 580, the pose relatedinformation, measured by the two tracking systems, and associated withthe same magnetic field flux measurement, may be fused to provide asingle pose related information measurement. The measurement of the twosystems may be fused, for example, according to a linear combination ofthe two measurements weighted by their respective noise variances or byapplying a Kalman filter as is known in the art. Consequently, processor562 also determines the pose (i.e., the location and orientation) offirst magnetic field detector 554 and of second magnetic field detector556 in optical coordinate system 574.

Similar to as described above, processor 562 estimates the magneticfield model by iteratively solving a determined or over-determined setof equations according to the magnetic field flux measurements and thepose related information respective of the selected first and secondportions of magnetic field flux measurements. The magnetic field fluxmeasurements with no respective pose related information are alsoemployed when estimating the magnetic field model similar to asdescribed above. Also, pose parameters, which are not included in poserelated information respective of the portion of magnetic field fluxmeasurements, may also be unknowns to be solved. Consequently, themagnetic field model is estimated in optical coordinate system 574.

As mentioned above, processor 562 does not need any prior knowledge ofthe magnetic field model. Processor 562 needs prior knowledge relatingonly to the template of the model, for example, harmonic functions suchas spherical harmonics, cylindrical harmonics or elliptical harmonicsFourier series and the like. Processor 562 estimates not only thecoefficients of the model but also the degree of the model (e.g., thedegree of the polynomial, or the degree and the order of the sphericalharmonics), the location of the center of expansion of the model in theoptical coordinate system 574 and the number of centers of expansion.The location of the center of expansion of the model relates to thelocation of the magnetic field generator or generators as well as to andto passive magnetic field sources (e.g., metallic objects with eddycurrents induced therein). Furthermore, processor 562 does not need todetermine the absolute pose of each measurement of the magnetic flux inoptical coordinate system 574. Rather, it is sufficient for processor562 to determine the relative pose between the current and the previousmeasurements of the magnetic flux. In other words optical coordinatesystem 574 may be completely arbitrary. For example, the origin andorientation of optical coordinate system 574 may be determined accordingto the pose of the first measurement. It is also noted that fordetermining the order of the model, and the number and locations of thecenter of expansions, the poser related information respective of atleast one of the magnetic field flux measurements should include all thelocation pose parameters (i.e., x, y and z).

The optical tracking system in FIG. 9 exhibits an in-out-out-inconfiguration. Thus, the representation of moving light emitter 568,determined from the image acquired by second imager 566, is associatedwith two respective angles. Furthermore, each representation of eachfixed light emitters 570 ₁ and 570 ₂, determined from the image acquiredby first imager 564, is also associated with two respective angles.Accordingly a total of six measurements of angles are acquired. Theseangles, along with the known spatial relationship (i.e., relative pose)between fixed light emitters 570 ₁ and 570 ₂ and second imager 566, andthe known spatial relationship between moving light emitter 568 andfirst imager 564, define the above mentioned six equations with sixunknowns. Processor, 562 solves these equations to determine thelocation and orientation of freestanding mapping handle 558.

As mentioned above, a system according to the disclosed technique doesnot require any prior knowledge regarding the magnetic field model butrather, only the template of the model is known. For example, the modelis of the following template:

$\begin{matrix}{{\varphi\left( {r,\theta,\phi} \right)} = {{\sum\limits_{s = 1}^{S}{\sum\limits_{l = 0}^{L}{\sum\limits_{m = {- l}}^{l}{c_{l,m,s}\frac{Y_{l,m,s}\left( {\theta,\phi} \right)}{r^{l + 1}}}}}} + {b_{l,m,s} \cdot r^{l} \cdot {Y_{s,l,m}\left( {\theta,\phi} \right)}}}} & (4)\end{matrix}$wherein φ(r,θ,ϕ) is the magnetic potential at a point defined by thespherical coordinates r,θ,ϕ, S defines the number of expansion centers,L defines the degree of the model, m defines the order of the model,c_(l,m) and b_(l,m) are coefficients to be estimated and Y_(s,l,m)(θ,ϕ)is a set of spherical harmonic functions of degree l and order m andexpanded about expansion center s, which are known in the art (i.e., thelocation of the expansion center is included within Y_(s,l,m) (θ,ϕ)).The system according to the disclosed technique described hereinabove inconjunction with FIG. 8 and FIG. 9 (e.g., processor 510 in FIG. 8 andprocessor 612 in FIG. 9) estimates the entire set of model parameters ofthe magnetic field model template of equation (4), L and m inclusive, aswell as the number of expansion centers S and their respectivelocations. The magnetic field is described by the gradient of φ(r,θ,ϕ):{right arrow over (B)}=−∇φ(r,θ,ϕ)  (5)Thus, even if no prior knowledge regarding the magnetic field in thevolume of interest exist, the system according to the disclosedtechnique may still determine a model of the magnetic field within thatvolume of interest.

According to another example, the magnetic field model exhibits thefollowing template:

$\begin{matrix}{{f(\xi)} = {{{M(\xi)} \cdot \Theta_{M}} = {\sum\limits_{s = 1}^{S}{\sum\limits_{l = 0}^{L}\left\lbrack {{M_{l}\left( {{- r^{(s)}} + r^{0}} \right)} \cdot \Theta_{l}^{({Ts})}} \right\rbrack}}}} & (6)\end{matrix}$where ξ represents the position of the sensor, L defines the degree ofthe model, S defines the number of expansion centers, M(ξ) representsthe spherical harmonics mode matrices and Θ_(M) represents thecoefficients matrices respective of each matrix M. Accordingly,M_(l)(−r^((s))+r⁰) is spherical harmonics mode matrices and Θ_(l)^((Ts)) is the respective coefficient matrix where r^((s)) representsthe distance of the expansion center of the matrix from the origin(e.g., of optical coordinate system 516) and r⁰ represents the distanceof the magnetic field detector from the origin. Similar to as describedabove, the system according to the disclosed technique describedestimates not only Θ_(M) but also M (i.e., size and entries), L and thenumber of expansion centers S and their respective locations.

A system according to the disclosed technique employs, for example, theleast squares method for estimating the entire set of parameters of themagnetic field model. A magnetic field model which fits, for example,one of the above templates described in equation (5) and (6), isestimated according to the deviations between the measurements of themagnetic field flux and predictions of the magnetic field flux, at therespective reference poses of each measurement (i.e., as determined bythe optical tracking system). For example, the magnetic field model isestimated by minimizing the sum of squared differences between themeasurements of the magnetic field flux and predictions of the magneticfield flux, at the respective reference poses of each measurement (i.e.,minimizing the L²-norm of the error). Alternatively, the L¹-norm or theL^(∞)-norm may be minimized.

To determine the order of the model the number of expansion centers andlocations of the expansion center, the system according to the disclosedtechnique, iteratively increases the number of expansion centers and theorder of the model and determines if the estimated model converges.(e.g., according to a FOM described above in equation (3)). For example,starting with a first order model and single center of expansion, thesystem estimates the parameters of the magnetic field model includingthe location of the center of expansion. If the FOM describedhereinabove in conjunction with equation (3) increases, then the systemdetermines that the estimated model does not converge (i.e., diverge).If the estimated model does not converge, the system increases the orderof the model and attempts to estimate the parameters of the model again.The system continues to increase the order of the model until a FOMreaches a determined threshold or until the estimated model begins todiverge relative to previous estimated orders (i.e., due to the systemnoise). If the estimated model begins to diverge and the FOM has yet toreach the determined threshold, an additional expansion center is addedto the model and the process repeats.

When estimating a magnetic field model according to the disclosedtechnique, as described above in conjunction with FIGS. 1-9, the volumeof interest is generally larger than the volume in which the objectbeing tracked is expected to move. In other words, the volume ofinterest is larger than the expected motion box of the object beingtracked. For example, the volume of interest is the cockpit of anaircraft and the object being tracked is the helmet of the pilot. Thus,the motion box is only the region with in the cockpit in which thehelmet of the pilot is expected to move. Since the accuracy of theestimated model deteriorates at the boundaries of the model, estimatingthe magnetic field within a volume of interest which is larger than theexpected motion box of the object being tracked, increases the accuracyof the a magnetic tracking system which employs the estimated magneticfield model, at the boundaries of the motion box. Alternatively,estimating the magnetic field within a volume of interest which islarger than the expected motion box of the object being tracked enablestracking a magnetic field detector event when that detector is locatedoutside the expected motion box.

Reference is now made to FIGS. 10A and 10B which are schematicillustrations of methods for estimating an entire set of parameter of amagnetic field model in accordance with a further embodiment of thedisclosed technique. In procedure 650, a magnetic field model templateis determined. This magnetic field model template is, for example, themagnetic field model template described herein above in equation (4) orin equation (6).

In procedure 652, a volume of interest is determined. When estimating amagnetic field model according to the disclosed technique, the volume ofinterest is larger than the expected motion box of the object beingtracked. Thus, the motion box is only a region with in the volume ofinterest in which the object being tracked is expected to move. Sincethe accuracy of the estimated model deteriorates at the boundaries ofthe model, estimating the magnetic field within a volume of interest,which is larger than the expected motion box of the object beingtracked, increases the accuracy of the a magnetic tracking system whichemploys the estimated magnetic field model, at the boundaries of themotion box and allows tracking a magnetic field sensors that is locatedoutside the motion box. With reference to FIGS. 8 and 9, volume ofinterest 518 (FIG. 8) and volume of interest 578 are determined as thevolume of interest

In procedure 654, a freely moving a magnetic field detector is movedwithin the determined volume of interest. The magnetic field detectorsmay be moved within the volume of interest at a random trajectory.Alternatively, the magnetic field detectors may be freely guided towardsregions of interest within the volume of interest. With reference toFIGS. 8 and 9, a user freely moves freestanding mapping handle 506 (FIG.8) and freestanding mapping handle 558 (FIG. 9), each of which includeat least one magnetic field detector attached thereto (i.e., magneticfield detector 504 in FIG. 8 and magnetic field detector 554 and 556 inFIG. 9).

In procedures 656 measurements of the magnetic field flux are acquiredat a plurality of locations and orientations of the freestandingmagnetic field detector within the volume of interest. With Reference toFIGS. 8, magnetic field detector 504 acquires measurements of themagnetic field flux at a plurality of locations and orientationsthereof. With reference to FIG. 9, detector 554 and 556 in FIG. 9)acquire measurements of the magnetic field flux at a plurality oflocations and orientations thereof.

In procedure 658, pose related information, respective at least aportion of the measurement of magnetic field flux, is determined. Thispose related information is determined by an additional tracking system.The additional tracking system may be an optical tracking system, aninertial tracker, an ultrasound tracker, a mechanical tracking system orany combination thereof which provides the additional informationrelating to the pose of the freestanding mapping handle and thus of themagnetic field detector. This pose related information may be employedas constraints when estimating the parameters characterizing themagnetic field model. For example, the additional tracking system mayprovide information relating only to selected pose parameters. Theseselected pose parameters may be selected location coordinates (i.e.,either x, y or z or any combination thereof), selected orientationangles (i.e., either azimuth, elevation or roll or any combinationthereof) or a selected combination of location coordinates andorientation angles (e.g., x, azimuth and elevation; y, z and roll; x, y,azimuth and elevation and the like). The selected pose parameters mayalso relate to all the pose parameters (i.e., x, y, z, azimuth,elevation and roll).

The pose related information respective of the portion of magnetic fieldflux measurement may include information relating to only the selectedpose parameters (i.e., selected location coordinates or selectedorientation angles or a selected combination of location coordinates andorientation angles) at each of the selected magnetic field fluxmeasurements. Additionally or alternatively, the information relating tothe pose of the magnetic field flux measurement may include informationrelating to a set of locations or a set of orientations or a set ofcombinations of location and orientation. For example, a set oflocations is a line (i.e., in the coordinate system associated with theadditional tracking system) on which the magnetic field flux measurementis located. Furthermore, the pose related information of each of theportion of magnetic field flux measurement may include different poseparameters. For example, one measurement is associated only withlocation, another measurement is associated only with orientation, yetanother measurement is associated with a line on which the measurementwas acquired and yet another measurement is associated with location andorientation. With reference to FIG. 8, the optical tracking system,defined by imager 512, light emitters 514 ₁, 514 ₂, 514 ₃ and processor510 determines pose related information respective of a portion of themagnetic field flux measurements acquired by magnetic field detector504. With reference to FIG. 9, first imager 564, second imager 566,light emitter 568, light emitters 570 ₁, 570 ₂, and processor 562 definean optical tracking system. Inertial sensor and processor 562 define aninertial tracking system. This combination of tracking systems determinepose related information respective of a portion of magnetic field fluxmeasurements acquired by magnetic field detectors 554 and 556.

In procedure 660, the entire set of parameters characterizing themagnetic field model is estimated according to the magnetic field fluxmeasurements and the pose related information respective of the portionof magnetic field flux measurements. This entire set includes thecoefficients of the model as well as the order of the model, the numberexpansion centers of the model and the location of the expansioncenters. Once the entire set of parameters is estimated these parametersare incorporated into the magnetic field model template thus definingthe estimated magnetic field model. It is noted that the magnetic fieldflux measurements with no respective pose related information are alsoemployed when estimating the magnetic field model. For example, pose ofthese measurements may also be unknowns to be solved, when a sufficientnumber of measurements with respective pose related information areacquired. Also, pose parameters, which are not included in pose relatedinformation respective of the portion of magnetic field fluxmeasurements, may also be unknowns to be solved. It is also noted thatfor determining the order of the model, and the number and locations ofthe center of expansions, the poser related information respective of atleast one of the magnetic field flux measurements should include all thelocation pose parameters (i.e., x, y and z). With reference to FIG. 8,processor 510 estimates the entire set of parameters characterizing themagnetic field model. With reference to FIG. 9, process 562 estimatesthe entire set of parameters characterizing eh magnetic field model.Estimating the entire set of parameters is further elaborated inconjunction with FIG. 10B.

With reference to FIG. 10B, in procedure 680, the parameterscharacterizing the magnetic field model, with the current order and thecurrent number of expansion centers, are iteratively estimated.Initially, the current order and the current number of expansion centersexhibit selected initial values. The location or locations of theexpansion center or centers are parameters to be estimated. Theparameters of the magnetic field model are estimated, for example, byemploying the least squares method. With reference to FIG. 8, processor510 iteratively estimates the parameters characterizing the magneticfield model. Similarly, with reference to FIG. 9, processor 562iteratively estimates the parameters characterizing the magnetic fieldmodel.

In procedure 682, a FOM is determined for each iteration of the magneticfield model estimation. This FOM is, for example, the FOM describedhereinabove in equation (3). When the FOM decreases, the model isdetermined to converge. When the FOM increases, the model is determinedto diverge. With reference to FIG. 8, processor 510 determines the FOMof the estimated magnetic field model. Similarly, with reference to FIG.9, determines the FOM of the estimated magnetic field model. When themagnetic field model is determined to diverge, designated ‘DIV.’ in FIG.10B then, the method proceeds to Procedure 684. When the FOM isdetermined to reach a determined threshold, designated ‘TSH.’ in FIG.10B then, the method proceeds to Procedure 692.

In procedure 684, the order of the magnetic field model is increased.With reference to FIGS. 8 and 9 processor 510 and processor 562respectively increase the order of the magnetic field model.

In procedure 686, the parameters characterizing the increased ordermagnetic field model are iteratively estimated. With reference to FIG.8, processor 510 iteratively estimates the parameters characterizing theincreased order magnetic field model. Similarly, with reference to FIG.9, processor 562 iteratively estimates the increased order parameterscharacterizing the magnetic field model.

In procedure 688, a FOM is determined for each iteration of the magneticfield model estimation. When the FOM increases, the model is determinedto diverge. With reference to FIG. 8, processor 510 determines the FOMof the estimated magnetic field model. Similarly, with reference to FIG.9, determines the FOM of the estimated magnetic field model. When thenew increased order magnetic field model is determined to diverge,designated ‘DIV.’ in FIG. 10B then, the method proceeds to Procedure690. When the FOM is determined to reach a determined threshold,designated ‘TSH.’ in FIG. 10B then, the method proceeds to Procedure692.

In procedure 690, an expansion center is added to the magnetic fieldmode and the order of the magnetic field model is reduce back to theinitial value. With reference to FIGS. 8 and 9 processor 510 andprocessor 562 respectively add an expansion center is added to themagnetic field mode and reduce the order of the magnetic field model tothe initial value. The method returns to Procedure 680.

In procedure 692, the parameters characterizing the magnetic field modelare incorporated into the magnetic field model template, thus definingthe magnetic field model. With reference to FIGS. 8 and 9 processor 510and processor 562 respectively incorporated the parameterscharacterizing the magnetic field model into the magnetic field modeltemplate.

In general, the magnetic field mapping systems described hereinabove inconjunction with FIGS. 1-5, the magnetic field sensors or magnetic fielddetectors should be calibrated. In other words, parameters relating tothe magnetic field sensors or magnetic field detectors should be known.For example, the parameters of a magnetic field sensor such as a coilmay include the cross-sectional area of the coil, the number of turns,the length, the resistance, the capacitance, the inductance and theQ-factor of the coil. The parameters of a magnetic field detectorincluding several coils may include the relative location andorientation between coils and the mutual inductance between the coils inaddition to the parameters relating to each coil.

The magnetic field mapping systems described hereinabove in conjunctionwith FIGS. 8 and 9 may further be employed to calibrate the magneticfield sensors and detectors employed thereby. In general, the parametersrelating to the magnetic field detectors and sensors included thereinare introduced to the magnetic field model as parameters to beestimated. For example, when considering only the cross-sectional areaA, the number of turns N and the resistance R of a coil, the magneticfield B, inducing a current I in the coil may be given by:

$\begin{matrix}{B = {\int{\frac{{- I}\; R}{N\; A}\cos\;\alpha\;{dt}}}} & (7)\end{matrix}$where α is the angle between the coil axis and the magnetic field fluxlines. Accordingly, in the mapping systems described above inconjunction with FIGS. 8 and 9, instead of evaluating B from givenvalues of the parameters relating to the magnetic field sensors anddetectors (e.g., A, N and R in equations (6)) and the measured current,the system estimates the parameters of both the magnetic field model andthe parameters relating the magnetic field detectors and sensorsyielding the resulting current measurements. In general the number ofmeasurements should at least equal the number of unknowns (i.e., modelparameters, sensor parameters and detector parameters).

The systems according to the disclosed technique described hereinabovein conjunction with FIGS. 8 and 9 do not necessarily estimate theparameters relating the magnetic field detectors and sensors during themapping but rather only when needed. For example, when the magneticfield model estimation process does not converge to a solution (e.g.,after a predetermined number of iterations), then, processor 510 (FIG.8) and processor 562 (FIG. 9) may introduce one or more of theparameters relating the either the magnetic field detectors or themagnetic field sensors or both to the magnetic field model estimationprocess. As a further example, if during before or during the mappingprocess the mapping handle was inflicted with a mechanical shock (e.g.,due to a fall or miss-handling by the user) then user may direct thesystem to include introduce one or more of the parameters relating theeither the magnetic field detectors or the magnetic field sensors orboth to the magnetic field model estimation process.

It will be appreciated by persons skilled in the art that the disclosedtechnique is not limited to what has been particularly shown anddescribed hereinabove. Rather the scope of the disclosed technique isdefined only by the claims, which follow.

The invention claimed is:
 1. A system for mapping a magnetic field in avolume of interest, the system comprising: a magnetic field transmitter,generating a magnetic field in said volume of interest; at least onefreestanding magnetic field detector, operative to freely move withinsaid volume of interest, said at least one freestanding magnetic fielddetector acquiring measurements of flux of said magnetic field at aplurality of poses; an optical tracking system for measuring informationrelated to the pose of said freestanding magnetic field detector; and aprocessor, coupled with said magnetic field detector and with saidoptical tracking system, said processor determining pose relatedinformation respective of at least a portion of said measurements of theflux of said magnetic field according to said information related to thepose of said freestanding magnetic field detector, measured by said atoptical tracking system, said processor estimating the entire set ofparameters of a magnetic field model template according to said magneticfield flux measurement and the respective pose related informationthereof, said processor incorporating said entire set of parameters intosaid magnetic field model template, thereby determining said magneticfield model, wherein, said entire set of parameters includes thecoefficients of said magnetic field model, the order of said magneticfield model, the number of the centers of expansion and the locations ofthem centers of expansion of said magnetic field model; and wherein,said centers of expansion of said magnetic field model relate to atleast one magnetic field generator.
 2. The system according to claim 1,wherein said optical tracking system includes at least one imager and atleast one light emitter.
 3. The system according to claim 2, furtherincluding an inertial tracking sensor coupled with said processor, alsofor measuring information related to the pose of said freestandingmagnetic field detector, said processor determining pose relatedinformation respective of at least a first portion of said measurementsaccording to said information related to the pose of said freestandingmagnetic field detector measured by said optical tracking system, saidprocessor determining pose related information respective of at least asecond portion of said measurements according to said informationrelated to the pose of said freestanding magnetic field detectormeasured by said inertial tracking sensor.
 4. The system according toclaim 3, wherein said first portion of measurements and said secondportion measurements are one of: mutually exclusive; partially overlap;and completely overlap.
 5. The system according to claim 3, wherein saidprocessor fuses said pose related information respective of ameasurement acquired from the optical tracking system with the poserelated information respective of said measurement acquired by saidinertial tracking sensor.
 6. The system according to claim 2, whereineach one of said at least one imager and each one of said at least onelight emitter is adapted to be fixedly coupled with said freestandingmagnetic field detector and with a reference location in said opticalcoordinate system.
 7. The system according to claim 6, including atleast two imagers and at least two light emitters, each of said at leasttwo imagers is adapted to be fixedly couple with a respective differentone of said magnetic field detector and said reference location.
 8. Thesystem according to claim 1, wherein said pose related informationrespective of at least a portion of said measurements includesinformation relating to only selected pose parameters.
 9. The systemaccording to claim 8, wherein said pose related information of each ofthe portion of magnetic field flux measurement may include differentpose parameters.
 10. The system according to claim 1, wherein said poserelated information respective of at least a portion of saidmeasurements includes information relating to one of a set of locations,a set of orientations and a set of combinations of location andorientation.
 11. The system according to claim 1, wherein said processoremploys said pose related information respective of at least a portionof said measurements as constraints when estimating the parameterscharacterizing said magnetic field model.
 12. The system according toclaim 1, further including a freestanding mapping handle operative tofreely move within said volume of interest, said at least onefreestanding magnetic field detector being coupled with saidfreestanding mapping handle.
 13. The system according to claim 1,wherein said at least one freestanding magnetic field detector is movedwithin said volume of interest at a random trajectory.
 14. The systemaccording to claim 1, wherein said at least one freestanding magneticfield detector is moved within said volume of interest through aplurality of mapping regions.
 15. The system according to claim 1,wherein said processor is further coupled with said magnetic fieldtransmitter.
 16. The system according to claim 1, wherein said systemcomprises at least two magnetic field detectors.
 17. The systemaccording to claim 16 wherein each of said magnetic field detectorsincludes three magnetic field sensors.
 18. The system according to claim16, wherein the spatial relationship between said two magnetic fielddetectors is known.
 19. The system according to claim 1, wherein saidmagnetic field transmitters includes three magnetic field generators.20. The system according to claim 1, wherein said centers of expansionfurther relate to at least one passive magnetic field source.
 21. Amethod for mapping a magnetic field in a volume of interest, the methodcomprising procedures of: freely moving a magnetic field detector withinsaid determined volume of interest; acquiring measurements of magneticfield flux at a plurality of poses of said freestanding magnetic fielddetector within said volume of interest; determining pose relatedinformation respective of at least a portion of said measurement ofmagnetic field flux by an optical tracking system; and estimating theentire set of parameters characterizing the magnetic field modelaccording to said magnetic field flux measurements and said respectivepositions and orientations thereof, wherein, said entire set ofparameters includes the coefficients of said magnetic field model, theorder of said magnetic field model, the number of the centers ofexpansion and the locations of the centers of expansion of said magneticfield model; and wherein, said centers of expansion of said magneticfield model relate to at least one magnetic field generator.
 22. Themethod according to claim 21, further including a preliminary procedureof determining a determining a magnetic field model template.
 23. Themethod according to claim 21, further including a preliminary procedureof determining a volume of interest.
 24. The method according to claim21, wherein said pose related information respective of at least aportion of said measurements includes information relating to onlyselected pose parameters.
 25. The method according to claim 24, whereinsaid pose related information of each of the portion of magnetic fieldflux measurement may include different pose parameters.
 26. The methodaccording to claim 21, wherein said pose related information respectiveof at least a portion of said measurements includes information relatingto one of a set of locations, a set of orientations and a set ofcombinations of location and orientation.
 27. The method according toclaim 21, wherein said processor employs said pose related informationrespective of at least a portion of said measurements as constraintswhen estimating the parameters characterizing said magnetic field model.28. The method according to claim 21, wherein said centers of expansionfurther relate to at least one passive magnetic field source.